%%
%% This is file `pstricks-add.tex',
%%
%% IMPORTANT NOTICE:
%%
%% Package `pstricks-add.tex'
%%
%% Herbert Voss <voss _at_ pstricks.de>
%%
%% This program can be redistributed and/or modified under the terms
%% of the LaTeX Project Public License Distributed from CTAN archives
%% in directory macros/latex/base/lppl.txt.
%%
%% DESCRIPTION:
%%   `pstricks-add' is a PSTricks package for additionals to the standard
%%         pstricks package
%%
\csname PSTricksAddLoaded\endcsname
\let\PSTricksAddLoaded\endinput
%
% Requires some packages
\ifx\PSTricksLoaded\endinput\else\input pstricks \fi
\ifx\PSTplotLoaded\endinput\else\input pst-plot \fi
\ifx\PSTnodesLoaded\endinput\else\input pst-node \fi
\ifx\MultidoLoaded\endinput\else\input multido \fi
\ifx\PSTXKeyLoaded\endinput\else\input pst-xkey \fi
%
\def\fileversion{2.73}
\def\filedate{2005/12/28}
\message{`pstricks-add' v\fileversion, \filedate\space (hv)}
%
\edef\PstAtCode{\the\catcode`\@} \catcode`\@=11\relax
\SpecialCoor
\pst@addfams{pstricks-add}
%
%% prologue for postcript
\pstheader{pstricks-add.pro}%
%\pstheader{shfill_emulate.pro}%
%
%
%-------------------------------- pstricks ------------------------------------
%
%%%%%%% \begin{pspicture} %%%%%%%%%%%%%%%%%%%
\newdimen\pst@dimm%
\newdimen\pst@dimn%
\newdimen\pst@dimo%
\newdimen\pst@dimp%
\newcount\pst@cntm%
\newcount\pst@cntn%
\newcount\pst@cnto%
\newcount\pst@cntp%
%\psset{dx=0}%
%\psset{dy=0}%
\newcount\@zero\@zero=0\relax
%
\def\pst@getdimdim#1 #2 #3\@nil{%
  \def\pst@tempA{#2}%
  \ifx\pst@tempA\@empty
    \pssetlength\pst@dimn{#1}%
    \pst@dimm=\z@%
  \else%
    \pssetlength\pst@dimm{#1}%
    \pssetlength\pst@dimn{#2}%
  \fi%
}
\def\pst@getxdimdim#1 #2 #3\@nil{%
  \def\pst@tempA{#2}%
  \ifx\pst@tempA\@empty
    \pssetxlength\pst@dimn{#1}%
    \pst@dimm=\z@
  \else%
    \pssetxlength\pst@dimm{#1}%
    \pssetxlength\pst@dimn{#2}%
  \fi%
}
\def\pst@getydimdim#1 #2 #3\@nil{%
  \def\pst@tempA{#2}
  \ifx\pst@tempA\@empty
    \pssetylength\pst@dimn{#1}
    \pst@dimm=\z@
  \else
    \pssetylength\pst@dimm{#1}%
    \pssetylength\pst@dimn{#2}%
  \fi%
}
%
% A modulo macro for integer values
% \pst@mod{34}{6}\value ==> \value is 4
%
\def\pst@mod#1#2#3{%
  \begingroup%
  \pst@cntm=#1\pst@cntn=#2\relax%
  \pst@cnto=\pst@cntm%
  \divide\pst@cntm by \pst@cntn%
  \multiply\pst@cntn by \pst@cntm%
  \advance\pst@cnto by -\pst@cntn%
  \edef\value{\endgroup\def\noexpand#3{\number\pst@cnto}}\value%
}
\def\pst@max#1#2#3{%
  \begingroup%
  \pst@cntm=#1\pst@cntn=#2\relax%
  \ifnum\pst@cntm<\pst@cntn\pst@cntm=\pst@cntn\fi
  \global#3=\the\pst@cntm%
  \endgroup%
}
\def\pst@maxdim#1#2#3{%
  \begingroup%
  \pst@dimm=#1\pst@dimn=#2\relax%
  \ifdim\pst@dimm<\pst@dimn\pst@dimm=\pst@dimn\fi
  \global#3=\the\pst@dimm%
  \endgroup%
}
\def\pst@abs#1#2{%
  \begingroup%
  \pst@cntm=#1\relax%
  \ifnum\pst@cntm<\z@\pst@cntm=-\pst@cntm\fi%
  \global#2=\the\pst@cntm
  \endgroup%
}
\def\pst@absdim#1#2{%
  \begingroup%
  \pst@dimm=#1\relax%
  \ifdim\pst@dimm<\z@\pst@dimm=-\pst@dimm\fi%
  \global#2=\the\pst@dimm%
  \endgroup%
}
%
%--------------------------------------- small stuff -------------------------------
\def\defineTColor{\@ifnextchar[{\defineTColor@i}{\defineTColor@i[]}}
\def\defineTColor@i[#1]#2#3{%     transparency "colors"
  \def\pst@tempA{#1}%
  \newpsstyle{#2}{%
     fillstyle=vlines,hatchwidth=0.1\pslinewidth,
     hatchsep=1\pslinewidth,hatchcolor=#3}%
  \ifx\pst@tempA\@empty\else\psset{#1}\fi%
}
\defineTColor{TRed}{red}
\defineTColor{TGreen}{green}
\defineTColor{TBlue}{blue}
%
\def\rmultiput{\def\pst@par{}\pst@ifstar{\@ifnextchar[{\rmultiput@i}{\rmultiput@i[]}}}
\def\rmultiput@i[#1]{\begingroup\psset{#1}\rmultiput@ii}
\def\rmultiput@ii#1{\def\@rmultiputArg{#1}%
  \@ifnextchar({\rmultiput@iii}{\rmultiput@iii(\z@,\z@)}}
\def\rmultiput@iii(#1){%
  \pst@killglue%
  \if@star\rput*(#1){\@rmultiputArg}
  \else\rput(#1){\@rmultiputArg}%
  \fi
  \@ifnextchar({\rmultiput@iii}{\endgroup}%
}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%    \psrotation(x,y){a}{objet}    %%%
%%% construit l'image de <objet>     %%%
%%% par la rotation de centre (x,y)  %%%
%%% et d'angle a.                    %%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\def\psrotate{\pst@object{psrotate}} % idea from Jean-C�e Charpentier
\def\psrotate@i(#1,#2)#3#4{%
  \pst@killglue
  \begin@SpecialObj%
  \addto@pscode{%
    #1 \pst@number\psxunit mul #2 \pst@number\psyunit mul translate
    #3 rotate -1 -1 scale 
    #1 \pst@number\psxunit mul #2 \pst@number\psyunit mul translate
    -1 -1 scale
  }%
  #4% 
  \end@SpecialObj%
}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Begin patch TN; Date (YY-MM-DD): 04-07-17; first part
\define@key[psset]{}{dash}{%	defined in pstricks.tex
  \pst@expandafter\psset@@dash{#1}\@nil% Error handling for empty argument.
}
\define@key[psset]{}{maxdashes}{\def\psk@maxdashes{#1}}
%\psset{maxdashes=11}
\def\psset@@dash#1\@nil{%
 \def\psk@dash{}%
 % modification 04-08-07:
 \pst@cntm0
 \def\next##1 ##2\relax{%
   \expandafter\ifnum\psk@maxdashes>\pst@cntm\relax% 04-08-07
   \edef\@tempa{##1}%
   \ifx\@tempa\@empty\else% gobble leading spaces
   \pssetlength\pst@dimc{##1}%
       \advance\pst@cntm by 1
   \edef\psk@dash{\psk@dash\space\pst@number\pst@dimc}%
   \fi%
   \edef\@tempa{##2}%
   \ifx\@tempa\@empty\else% detect end
   \ifx\@tempa\space\else% gobble trailing spaces
     \next##2\relax%
   \fi\fi%
   \else% 04-08-07
     \@pstrickserr{Number of dashes > \psk@maxdashes. Increasing
`maxdashes' might work.}\@ehpa% 04-08-07
   \fi% 04-08-07
 }%
\expandafter\next#1 \relax}
%% End patch TN; Date (YY-MM-DD): 04-07-17; 1st part
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%\psset{dash=5pt 3pt}% black white black white 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Begin patch TN; Date (YY-MM-DD): 04-07-17; 2nd part
\def\psls@dashed{%
  \ifpsdashadjust
    [ \psk@dash ] \@ifundefined{pst@linetype}{2}{\pst@linetype}\space \tx@DashLine
  \else
    [ \psk@dash ] 0 setdash stroke
  \fi}
%% End patch TN; Date (YY-MM-DD): 04-07-17; 2nd part
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%-----------------------------------------------------------------------------------
\pst@def{DashLine}<
    dup 0 gt
    { /a .5 def PathLength exch div }
    { pop /a 1 def PathLength } ifelse
    /b ED % pattern should fit evenly in b
    dup /X ED % pattern array
    0 get /y ED % length of first black segment
    /z 0 X {add} forall def % length of the full pattern
    %% Computation of the scaling factor as described by van Zandt:
    b a .5 sub 2 mul y mul sub z Div round
    z mul a .5 sub 2 mul y mul add b exch Div
    %%%% scaling factor on stack.
    /z ED %% now, z is the scaling factor
    false % for the length test below
    X { z mul } forall X astore %% modification TN 04-08-07
    %%% Checking whether at least one dash in X has positive length:
    {0 gt or} forall
    { X 1 a sub y mul }
    { [ 1 0 ] 0 }
    ifelse
    setdash stroke >
%% TN end patch; Date (YY-MM-DD): 04-07-17;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%
\define@key[psset]{}{intSeparator}{\def\psk@intSeparator{#1}}
%\psset{intSeparator={,}}
%
\def\psFormatInt{\def\pst@par{}\pst@object{psFormatInt}}
\def\psFormatInt@i#1{{%
  \pst@killglue
  \use@par
  \count1=#1\count2=\count1
  \ifnum\count1=0 0\else
    \ifnum\count1>999999
    \count3=\count1
    \divide\count3 by 1000000
    \the\count3\psk@intSeparator\relax
    \multiply\count3 by 1000000
    \advance\count1 by -\count3 % modulo 1000000
  \fi%
  \ifnum\count2>999
    \count3=\count1
    \divide\count3 by 1000
    \ifnum\count2>99999
	\ifnum\count3<100 0\fi
	\ifnum\count3<10 0\fi
    \fi%
    \the\count3\psk@intSeparator\relax
    \multiply\count3 by 1000
    \advance\count1 by -\count3 %modulo 1000
  \fi%
  \ifnum\count2>999
    \ifnum\count1<100 0\fi
    \ifnum\count1<10 0\fi
  \fi%
  \the\count1
  \fi%
}\ignorespaces}
%
\newdimen\pst@braceWidth
\define@key[psset]{}{braceWidth}{\pssetlength\pst@braceWidth{#1}}
\define@key[psset]{}{bracePos}{\def\psk@bracePos{#1}}
%\psset{braceWidth=10pt,bracePos=0.5}
%
\def\@@rput@iv(#1){\pst@killglue\pst@makebox{\@@rput@v{#1}}}
\def\@@rput@v#1{%
  \begingroup
    \use@par
    \pst@makesmall\pst@hbox
    \pst@Verb{%
      Alpha 90 sub \pst@number\pst@braceWidth  0 lt {180 add} if
      \ifx\psk@rot\@empty\else\psk@rot add \fi
      /rotAngle exch def
    }%
    \setbox\pst@hbox=\hbox{%
      \pst@Verb{rotAngle \tx@RotBegin}%
      \box\pst@hbox\pst@Verb{\tx@RotEnd}%
    }%
    \psput@{#1}\pst@hbox
  \endgroup
  \ignorespaces%
}
%
\def\psbrace{\def\pst@par{}\pst@object{psbrace}}
\def\psbrace@i(#1)(#2)#3{%
  \addbefore@par{ArrowInside=-,linearc=2mm,linewidth=1pt,%
    nodesepA=0pt,nodesepB=0pt,bracePos=0.5}% the default
  \begin@SpecialObj
  \use@par%
  \pst@getcoor{#1}\pst@tempA%
  \pst@getcoor{#2}\pst@tempB%
  \pnode(!%
    /bW2 \pst@number\pst@braceWidth \pst@number\psyunit div 2.0 div def
    \pst@tempA /YA exch \pst@number\psyunit div def
    /XA exch \pst@number\psxunit div def
    \pst@tempB /YB exch \pst@number\psyunit div def
    /XB exch \pst@number\psxunit div def
    /Alpha YB YA sub XB XA sub atan def
    /xMid XB XA sub \psk@bracePos\space mul XA add def
    /yMid YB YA sub \psk@bracePos\space mul YA add def
    /@deltaX Alpha sin bW2 mul def
    /@deltaY Alpha cos bW2 mul def
    /@xTemp xMid @deltaX 2 mul add def
    /@yTemp yMid @deltaY 2 mul sub def
    @xTemp @yTemp){@tempNode}%
  \pst@getcoor{@tempNode}\pst@tempC%
  \@@rput@iv(! %
    \pst@tempC /Yc exch def
    /Xc exch def
    Xc \psk@nodesepA\space add \pst@number\psxunit div
    Yc \psk@nodesepB\space add \pst@number\psyunit div ){#3}
  \psline(#1)%
    (! XA @deltaX add YA @deltaY sub)%
    (! @xTemp @deltaX sub @yTemp @deltaY add)(@tempNode)%
  \psline(@tempNode)%
    (! @xTemp @deltaX sub @yTemp @deltaY add)%
    (! XB @deltaX add YB @deltaY sub)(#2)%
  \end@SpecialObj
  \ignorespaces}
%
% -------------- the arrow part -------------
%  the original table
% \def\pst@arrowtable{,<->,<<->>,>-<,>>-<<,(-),[-],)-(,]-[,|>-<|}
\edef\pst@arrowtable{\pst@arrowtable,H-H,h-h}
%
% HookLeft/RightArrow
\newdimen\pshooklength
\newdimen\pshookwidth
\define@key[psset]{}{hooklength}{\pssetlength\pshooklength{#1}}
\define@key[psset]{}{hookwidth}{\pssetlength\pshookwidth{#1}}
%\psset{hooklength=3mm,hookwidth=1mm}
%
\edef\pst@arrowtable{\pst@arrowtable,H-H,h-h} % add new arrow
\def\tx@RHook{RHook }         % PostScript name
\def\tx@Rhook{Rhook }         % PostScript name
\@namedef{psas@H}{%
  /RHook {
    /x ED                     % hook width
    /y ED                     % hook length 
    /z CLW 2 div def          % save it
    x y moveto                % goto first point
    x 0 0 0 0 y 
    curveto                   % draw Bezier
    stroke 
    0 y moveto                % define current point
  } def
  \pst@number\pshooklength
  \pst@number\pshookwidth
  \tx@RHook 
}
\@namedef{psas@h}{%
  /Rhook {
    CLW mul 			% size * CLW
    add dup 			% +length  size*CLW+length size*CLW+length 
    2 div /w ED	 		% (size*CLW+length)/2  -> w 
    mul dup /h ED mul 		% (size*CLW+length)
    /a ED  
    w neg h abs moveto 0 0 L 
    gsave 
    stroke grestore 
  } def
  0 \psk@arrowlength \psk@arrowsize \tx@Rhook 
}
% New parameter "arrowfill", with default as "true"
\newif\ifpsArrowFill
\define@key[psset]{}{ArrowFill}{\@nameuse{psArrowFill#1}}
%\psset{ArrowFill=true}

% Modification of the PostScript macro Arrow to choose to fill or not the arrow
% (it require to restore the current linewidth, despite of the scaling)
\pst@def{Arrow}<{%
    CLW mul add dup 2 div
    /w ED mul dup
    /h ED mul
    /a ED { 0 h T 1 -1 scale } if
    gsave
    \ifpsArrowFill\else\pst@number\pslinewidth \pst@arrowscale\space div SLW \fi
    w neg h moveto
    0 0 L w h L w neg a neg rlineto
    \ifpsArrowFill gsave fill grestore \else gsave closepath stroke grestore \fi
    grestore
    0 h a sub moveto
}>
%
\define@key[psset]{}{nArrowsA}{\def\psk@nArrowsA{#1}}
\define@key[psset]{}{nArrowsB}{\def\psk@nArrowsB{#1}}
\define@key[psset]{}{nArrows}{\def\psk@nArrowsA{#1}\def\psk@nArrowsB{#1}}
%\psset{nArrows=2}
%
\@namedef{psas@>>}{%
    \psk@nArrowsA\space 1 sub {
      false \psk@arrowinset \psk@arrowlength \psk@arrowsize \tx@Arrow
      0 h a sub T
    } repeat
    gsave
    newpath
    false \psk@arrowinset \psk@arrowlength \psk@arrowsize \tx@Arrow
    CP
    grestore
    moveto
}
%
\@namedef{psas@<<}{%
    true \psk@arrowinset \psk@arrowlength \psk@arrowsize \tx@Arrow
    0 h neg a add T
  \psk@nArrowsB\space 2 sub {
    false \psk@arrowinset \psk@arrowlength \psk@arrowsize \tx@Arrow
    0 h neg a add T
  } repeat
  false \psk@arrowinset \psk@arrowlength \psk@arrowsize \tx@Arrow
  0 h a 5 mul 2 div sub moveto
}
%
% DG addition begin - Dec. 18/19, 1997 and Oct. 11, 2002
% Adapted from \psset@arrows
\define@key[psset]{}{ArrowInside}{%
  \def\pst@tempA{#1}%
  \ifx\pst@tempA\@empty\def\psk@ArrowInside{}%
  \else%
    \begingroup%
      \pst@activearrows%
      \xdef\pst@tempg{<#1}%
    \endgroup%
    \expandafter\psset@@ArrowInside\pst@tempg\@empty-\@empty\@nil%
    \if@pst\else\@pstrickserr{Bad intermediate arrow specification: #1}\@ehpa\fi%
  \fi%
}
% Adapted from \psset@@arrows
\def\psset@@ArrowInside#1-#2\@empty#3\@nil{%
  \@psttrue
  \def\next##1,#1-##2,##3\@nil{\def\pst@tempg{##2}}%
  \expandafter\next\pst@arrowtable,#1-#1,\@nil
  \@ifundefined{psas@#2}%
    {\@pstfalse\def\psk@ArrowInside{}}%
    {\def\psk@ArrowInside{#2}}%
}
% Default value empty
%\psset{ArrowInside={}}
% Modified version of \pst@addarrowdef
\def\pst@addarrowdef{%
    \addto@pscode{%
	/ArrowA {
    	    \ifx\psk@arrowA\@empty
		\pst@oplineto
	    \else
		\pst@arrowdef{A}
		moveto
	    \fi
	} def
	/ArrowB {
	    \ifx\psk@arrowB\@empty \else \pst@arrowdef{B} \fi
	} def
% DG addition
	/ArrowInside {
	    \ifx\psk@ArrowInside\@empty \else \pst@arrowdefA{Inside} \fi
	} def
    }%
}
% Adapted from \pst@arrowdef
\def\pst@arrowdefA#1{%
  \ifnum\pst@repeatarrowsflag>\z@
    /Arrow#1c [ 6 2 roll ] cvx def Arrow#1c
  \fi
  \tx@BeginArrow
  \psk@arrowscale
  \@nameuse{psas@\@nameuse{psk@Arrow#1}}
  \tx@EndArrow%
}
% ArrowInsidePos parameter (default value 0.5)
\define@key[psset]{}{ArrowInsidePos}{\pst@checknum{#1}\psk@ArrowInsidePos}%
%\psset{ArrowInsidePos=0.5}
%
% Modified version of \begin@ClosedObj
\def\begin@ClosedObj{%
    \leavevmode
    \pst@killglue
    \begingroup
	\use@par
	\solid@star
	\ifpsdoubleline \pst@setdoublesep \fi
	\pst@addarrowdef% DG addition
	\init@pscode
}
%
% Redefinition of the PostScript /Line macro to print the intermediate
% arrow on each segment of the line
%
\define@key[psset]{}{ArrowInsideNo}{\pst@checknum{#1}\psk@ArrowInsideNo}% hv 20031001
\define@key[psset]{}{ArrowInsideOffset}{\pst@checknum{#1}\psk@ArrowInsideOffset}% hv 20031001
%\psset{ArrowInsideNo=1,ArrowInsideOffset=0}
%
\pst@def{Line}<{%
  NArray n 0 eq not { n 1 eq { 0 0 /n 2 def } if
  (\psk@ArrowInside) length 0 gt {
    2 copy /y1 ED /x1 ED ArrowA x1 y1
    /n n 1 sub def
    n {
      4 copy
      /y1 ED /x1 ED /y2 ED /x2 ED
      x1 y1
      \psk@ArrowInsidePos\space 1 gt {
        /Alpha y2 y1 sub x2 x1 sub atan def
        /ArrowPos \psk@ArrowInsideOffset\space def
        /Length x2 x1 sub y2 y1 sub Pyth def
        /dArrowPos \psk@ArrowInsidePos\space abs def
        {
          /ArrowPos ArrowPos dArrowPos add def
          ArrowPos Length gt { exit } if
          x1 Alpha cos ArrowPos mul add
          y1 Alpha sin ArrowPos mul add
          ArrowInside
          pop pop
        } loop
      }{
        /ArrowPos \psk@ArrowInsideOffset\space def
        /dArrowPos \psk@ArrowInsideNo 1 gt {%
          1.0 \psk@ArrowInsideNo 1.0 add div
        }{\psk@ArrowInsidePos } ifelse def
          \psk@ArrowInsideNo\space cvi {
            /ArrowPos ArrowPos dArrowPos add def
            x2 x1 sub ArrowPos mul x1 add
            y2 y1 sub ArrowPos mul y1 add
            ArrowInside
            pop pop
          } repeat
      } ifelse
      pop pop Lineto
    } repeat
  }{ ArrowA /n n 2 sub def n { Lineto } repeat } ifelse
  CP 4 2 roll ArrowB L pop pop } if%
}>
%
% Redefinition of the PostScript /Polygon macro to print the intermediate
% arrow on each segment of the line
\pst@def{Polygon}<{%
    NArray n 2 eq { 0 0 /n 3 def } if
    n 3 lt {
	n { pop pop } repeat
    }{
	n 3 gt { CheckClosed } if
	n 2 mul	-2 roll
	/y0 ED
	/x0 ED
    	/y1 ED
    	/x1 ED
    	/xx1 x1 def
    	/yy1 y1 def
    	x1 y1
    	/x1 x0 x1 add 2 div def
    	/y1 y0 y1 add 2 div def
    	x1 y1 moveto
    	/n n 2 sub def
	/drawArrows {
	    x11 y11
	    \psk@ArrowInsidePos\space 1 gt {
		/Alpha y12 y11 sub x12 x11 sub atan def
		/ArrowPos \psk@ArrowInsideOffset\space def
		/Length x12 x11 sub y12 y11 sub Pyth def
		/dArrowPos \psk@ArrowInsidePos\space abs def
		{
		    /ArrowPos ArrowPos dArrowPos add def
		    ArrowPos Length gt { exit } if
		    x11 Alpha cos ArrowPos mul add
		    y11 Alpha sin ArrowPos mul add
		    currentdict /ArrowInside known { ArrowInside } if
		    pop pop
		} loop
	    }{
		/ArrowPos \psk@ArrowInsideOffset\space def
		/dArrowPos \psk@ArrowInsideNo\space 1 gt {%
	    	    1.0 \psk@ArrowInsideNo\space 1.0 add div
		}{ \psk@ArrowInsidePos } ifelse def
		\psk@ArrowInsideNo\space cvi {
		    /ArrowPos ArrowPos dArrowPos add def
		    x12 x11 sub ArrowPos mul x11 add
		    y12 y11 sub ArrowPos mul y11 add
		    currentdict /ArrowInside known { ArrowInside } if
		    pop pop
		} repeat
	    } ifelse
	    pop pop Lineto
	} def
	n {
	    4 copy
	    /y11 ED /x11 ED /y12 ED /x12 ED
	    drawArrows
	} repeat
	x1 y1 x0 y0
	6 4 roll
	2 copy
	/y11 ED /x11 ED /y12 y0 def /x12 x0 def
	drawArrows
	/y11 y0 def /x11 x0 def /y12 yy1 def /x12 xx1 def
	drawArrows
	pop pop
    	closepath
    } ifelse %
}>
%
%
% Redefinition of the PostScript /OpenBezier macro to print the intermediate
% arrow
\pst@def{OpenBezier}<{%
  /dArrowPos \psk@ArrowInsideNo 1 gt {%
    1.0 \psk@ArrowInsideNo 1.0 add div
    }{ \psk@ArrowInsidePos } ifelse def
      BezierNArray
      n 1 eq { pop pop
      }{ 2 copy
        /y0 ED /x0 ED
        ArrowA
        n 4 sub 3 idiv { 6 2 roll 4 2 roll curveto } repeat
        6 2 roll
        4 2 roll
        ArrowB
        /y3 ED /x3 ED /y2 ED /x2 ED /y1 ED /x1 ED
        /cx x1 x0 sub 3 mul def
        /cy y1 y0 sub 3 mul def
        /bx x2 x1 sub 3 mul cx sub def
        /by y2 y1 sub 3 mul cy sub def
        /ax x3 x0 sub cx sub bx sub def
        /ay y3 y0 sub cy sub by sub def
        /getValues {
          ax t0 3 exp mul bx t0 t0 mul mul add cx t0 mul add x0 add
          ay t0 3 exp mul by t0 t0 mul mul add cy t0 mul add y0 add
          ax t 3 exp mul bx t t mul mul add cx t mul add x0 add
          ay t 3 exp mul by t t mul mul add cy t mul add y0 add
        } def
        /getdL {
          getValues
          3 -1 roll sub 3 1 roll sub Pyth
        } def
        /CurveLength {
          /u 0 def
          /du 0.01 def
          0 100 {
            /t0 u def
            /u u du add def
            /t u def
            getdL add
          } repeat } def
          /GetArrowPos {
            /ende \psk@ArrowInsidePos\space 1 gt
              {ArrowPos}
              {ArrowPos CurveLength mul} ifelse def
            /u 0 def
            /du 0.01 def
            /sum 0 def
            { /t0 u def
              /u u du add def
              /t u def
              /sum getdL sum add def
              sum ende gt {exit} if
            } loop u
          } def
          /ArrowPos \psk@ArrowInsideOffset\space def
          /loopNo \psk@ArrowInsidePos\space 1 gt {%
            CurveLength \psk@ArrowInsidePos\space div cvi
          }{ \psk@ArrowInsideNo } ifelse def
            loopNo cvi {
              /ArrowPos ArrowPos dArrowPos add def
              /t GetArrowPos def
              /t0 t 0.95 mul def
              getValues
              ArrowInside pop pop pop pop
            } repeat
            x1 y1 x2 y2 x3 y3 curveto
  } ifelse
}>
%
% Redefinition of the PostScript /NCLine macro to print the intermediate
% arrow of the line
\pst@def{NCLine}<{%
	NCCoor
	tx@Dict begin
	ArrowA CP 4 2 roll ArrowB
	4 copy
	/y2 ED /x2 ED /y1 ED /x1 ED
	x1 y1
	\psk@ArrowInsidePos\space 1 gt {
		/Alpha y2 y1 sub x2 x1 sub atan def
		/ArrowPos \psk@ArrowInsideOffset\space def
		/Length x2 x1 sub y2 y1 sub Pyth def
		/dArrowPos \psk@ArrowInsidePos\space abs def
		{%
			/ArrowPos ArrowPos dArrowPos add def
			ArrowPos Length gt { exit } if
			x1 Alpha cos ArrowPos mul add
			y1 Alpha sin ArrowPos mul add
			ArrowInside
			pop pop
		} loop
	}{%
		/ArrowPos \psk@ArrowInsideOffset\space def
		/dArrowPos \psk@ArrowInsideNo 1 gt {%
			1.0 \psk@ArrowInsideNo 1.0 add div
		}{ \psk@ArrowInsidePos } ifelse def
		\psk@ArrowInsideNo\space cvi {
			/ArrowPos ArrowPos dArrowPos add def
			x2 x1 sub ArrowPos mul x1 add
			y2 y1 sub ArrowPos mul y1 add
			ArrowInside
			pop pop
		} repeat
	} ifelse
	pop pop lineto pop pop
	end%
}>
%
\pst@def{NCCurve}<{%
	GetEdgeA GetEdgeB
	xA1 xB1 sub yA1 yB1 sub
	Pyth 2 div dup 3 -1 roll mul
	/ArmA ED
	mul
	/ArmB ED
	/ArmTypeA 0 def
	/ArmTypeB 0 def
	GetArmA GetArmB
	xA2 yA2 xA1 yA1
	2 copy
	/y0 ED /x0 ED
	tx@Dict begin
		ArrowA
	end
	xB2 yB2 xB1 yB1
	tx@Dict begin
		ArrowB
	end
	/y3 ED /x3 ED /y2 ED /x2 ED /y1 ED /x1 ED
	/cx x1 x0 sub 3 mul def
	/cy y1 y0 sub 3 mul def
	/bx x2 x1 sub 3 mul cx sub def
	/by y2 y1 sub 3 mul cy sub def
	/ax x3 x0 sub cx sub bx sub def
	/ay y3 y0 sub cy sub by sub def
	/getValues {
		ax t0 3 exp mul bx t0 t0 mul mul add cx t0 mul add x0 add
		ay t0 3 exp mul by t0 t0 mul mul add cy t0 mul add y0 add
		ax t 3 exp mul bx t t mul mul add cx t mul add x0 add
	ay t 3 exp mul by t t mul mul add cy t mul add y0 add
	} def
	/getdL {
		getValues
		3 -1 roll sub 3 1 roll sub Pyth
	} def
	/CurveLength {
		/u 0 def
		/du 0.01 def
		0 100 {
			/t0 u def
			/u u du add def
			/t u def
			getdL add
		} repeat } def
	/GetArrowPos {
		/ende \psk@ArrowInsidePos\space 1 gt {ArrowPos}{ArrowPos CurveLength mul} ifelse def
		/u 0 def
		/du 0.01 def
		/sum 0 def
		{
			/t0 u def
			/u u du add def
			/t u def
			/sum getdL sum add def
			sum ende gt {exit} if
		} loop u
	} def
	/dArrowPos \psk@ArrowInsideNo 1 gt {%
		1.0 \psk@ArrowInsideNo 1.0 add div
	}{ \psk@ArrowInsidePos } ifelse def
	/ArrowPos \psk@ArrowInsideOffset\space def
	/loopNo \psk@ArrowInsidePos\space 1 gt {%
		CurveLength \psk@ArrowInsidePos\space div cvi
		}{ \psk@ArrowInsideNo } ifelse def
	loopNo cvi {
		/ArrowPos ArrowPos dArrowPos add def
		/t GetArrowPos def
		/t0 t 0.95 mul def
		getValues
		ArrowInside pop pop pop pop
	} repeat
	x1 y1 x2 y2 x3 y3 curveto
	/LPutVar [ xA1 yA1 xA2 yA2 xB2 yB2 xB1 yB1 ] cvx def
	/LPutPos { t LPutVar BezierMidpoint } def
	/HPutPos { { HPutLines } HPutCurve } def
	/VPutPos { { VPutLines } HPutCurve } def
}>
%
%\def\psDashColorI{black}
%\def\psDashColorII{red}
\define@key[psset]{}{dashColorI}{\pst@getcolor{#1}\psDashColorI}
\define@key[psset]{}{dashColorII}{\pst@getcolor{#1}\psDashColorII}
\define@key[psset]{}{dashNo}{\def\psk@dashNo{#1}}
%
\define@key[psset]{}{linecap}{\def\psk@linecap{#1}}
%\psset{dashColorI=black,dashColorII=red,dashNo=0.2,linecap=0}
%
\pst@def{LineII}<{%
  NArray
  /n n 1 sub def
  /y1 ED /x1 ED x1 y1 ArrowA x1 y1 moveto
  \psk@linecap\space 3 gt
    {\psk@linecap\space 0 lt {0 setlinecap} if }
    {\psk@linecap\space setlinecap} ifelse
  n {
    /y2 ED /x2 ED
    /y0 y1 def /x0 x1 def
    /length x2 x1 sub y2 y1 sub Pyth def
    \psk@dashNo\space 1.0 lt
      {/cntMax 1.0 \psk@dashNo\space div .49 add cvi def}
      {/cntMax length \psk@dashNo\space div .49 add cvi def} ifelse
    x2 x1 sub cntMax div /dx ED
    y2 y1 sub cntMax div /dy ED
    /cnt 0 def
    cntMax {
      gsave
      /x1 x1 dx add def
      /y1 y1 dy add def
      x1 y1
      cnt 2 mod 0 eq
        { \pst@usecolor\psDashColorI }
	{ \pst@usecolor\psDashColorII } ifelse
      lineto stroke
      /cnt cnt 1 add def
      grestore
      x1 y1 moveto
    } repeat
    /y1 y2 def /x1 x2 def
  } repeat
  x0 y0 x2 y2 ArrowB L pop pop
}>
%
\def\pslineII{\pst@object{pslineII}}
\def\pslineII@i{%
    \pst@getarrows{%
        \begin@OpenObj
        \pst@getcoors[\pslineII@ii%
    }%
}
\def\pslineII@ii{%
  \addto@pscode{%
    \pst@cp
    \ifshowpoints true \else false \fi
    \tx@LineII
  }%
  \end@OpenObj%
}
%
\newdimen\pswBegin\newdimen\pswEnd
\define@key[psset]{}{wBegin}{\pssetlength\pswBegin{#1}}
\define@key[psset]{}{wEnd}{\pssetlength\pswEnd{#1}}
%\psset{wBegin=\pslinewidth, wEnd=\pslinewidth}
%
\pst@def{LineIII}<{%
	NArray
	/n n 1 sub def
	/YA ED /XA ED
	/bA2 \pst@number\pswBegin\space 2.0 div def
	/bB2 \pst@number\pswEnd\space 2.0 div def
	/xStep bB2 bA2 sub n div def
	0 setlinecap
	n {
		XA YA moveto
		/YB ED /XB ED
		/Alpha YB YA sub XB XA sub atan def
		/Alphasin Alpha sin def
		/Alphacos Alpha cos def
        \pst@usecolor\pslinecolor
		0.01 SLW
		/bB2 bA2 xStep add def
		XA Alphasin bA2 mul sub
		YA Alphacos bA2 mul add lineto
		XB Alphasin bB2 mul sub
		YB Alphacos bB2 mul add lineto
		XB Alphasin bB2 mul add
		YB Alphacos bB2 mul sub lineto
		XA Alphasin bA2 mul add
		YA Alphacos bA2 mul sub lineto
		XA YA lineto fill
		/XA XB def /YA YB def
		/bA2 bB2 def
	} repeat
}>
%
\def\pslineIII{\pst@object{pslineIII}}
\def\pslineIII@i{%
  \pst@getarrows{%
     \begin@OpenObj
       \pst@getcoors[\pslineIII@ii%
  }%
}
\def\pslineIII@ii{%
  \addto@pscode{%
    \pst@cp
    \ifshowpoints true \else false \fi
    \tx@LineIII
  }%
  \end@OpenObj%
}
%
\define@key[psset]{}{randomPoints}{\def\psk@randomPoints{#1}}
\newif\ifPst@randomColor
\define@key[psset]{}{color}[true]{\@nameuse{Pst@randomColor#1}}
%\psset{randomPoints=1000,color=false}
%
\def\psRandom{\pst@object{psRandom}}%  hv  2004-11-12
\def\psRandom@i{\@ifnextchar({\psRandom@ii}{\psRandom@iii(0,0)(1,1)}}
\def\psRandom@ii(#1){\@ifnextchar({\psRandom@iii(#1)}{\psRandom@iii(0,0)(#1)}}
\def\psRandom@iii(#1)(#2)#3{%
  \def\pst@tempA{#3}%
  \ifx\pst@tempA\pst@empty\psclip{\psframe(#2)}\else\psclip{#3}\fi
  \pst@getcoor{#1}\pst@tempA 
  \pst@getcoor{#2}\pst@tempB 
  \begin@SpecialObj
  \addto@pscode{
    \pst@tempA\space /yMin exch def 
    /xMin exch def
    \pst@tempB\space /yMax exch def 
    /xMax exch def 
    /dy yMax yMin sub def
    /dx xMax xMin sub def
    rrand srand                 % initializes the random generator
    /getRandReal { rand 2147483647 div } def
    \psk@dotsize % defines /DS ... def
    \@nameuse{psds@\psk@dotstyle}
    \psk@randomPoints {
     \ifPst@randomColor getRandReal getRandReal getRandReal setrgbcolor \fi
     getRandReal dx mul xMin add
     getRandReal dy mul yMin add
     Dot
     \ifx\psk@fillstyle\psfs@solid fill \fi stroke
    } repeat
  }%
  \end@SpecialObj
  \endpsclip
  \ignorespaces
}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%                                                  %%%%%%%%%%
%%%%%%%%%%%                pst-node                          %%%%%%%%%%
%%%%%%%%%%%                                                  %%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% This fixes a bug in pst-node, where the XY-direction is wrong
% the types are changed 1<->2 between X<->Y
%
\define@key[psset]{}{XnodesepA}{%
    \pst@getlength{#1}\psk@nodesepA
    \def\psk@nodeseptypeA{2 }%
}
\define@key[psset]{}{XnodesepB}{%
    \pst@getlength{#1}\psk@nodesepB
    \def\psk@nodeseptypeB{2 }%
}
\define@key[psset]{}{Xnodesep}{%
    \pst@getlength{#1}\psk@nodesepA
    \let\psk@nodesepB\psk@nodesepA
    \def\psk@nodeseptypeA{2 }%
    \def\psk@nodeseptypeB{2 }%
}
\define@key[psset]{}{YnodesepA}{%
    \pst@getlength{#1}\psk@nodesepA
    \def\psk@nodeseptypeA{1 }%
}
\define@key[psset]{}{YnodesepB}{%
    \pst@getlength{#1}\psk@nodesepB
    \def\psk@nodeseptypeB{1 }%
}
\define@key[psset]{}{Ynodesep}{%
    \pst@getlength{#1}\psk@nodesepA
    \let\psk@nodesepB\psk@nodesepA
    \def\psk@nodeseptypeA{1 }%
    \def\psk@nodeseptypeB{1 }%
}
%
\pst@def{NCLineII}<{
  NCCoor
  /y1 ED /x1 ED x1 y1 ArrowA x1 y1 moveto
  /y2 ED /x2 ED
  /y0 y1 def /x0 x1 def
  /length x2 x1 sub y2 y1 sub Pyth def
  \psk@dashNo\space 1.0 lt
     {/cntMax 1.0 \psk@dashNo\space div .49 add cvi def}
     {/cntMax length \psk@dashNo\space div .49 add cvi def} ifelse
  x2 x1 sub cntMax div /dx ED
  y2 y1 sub cntMax div /dy ED
  /cnt 0 def
  cntMax {
    gsave
    /x1 x1 dx add def
    /y1 y1 dy add def
    x1 y1
    cnt 2 mod 0 eq
      { \pst@usecolor\psDashColorI }
      { \pst@usecolor\psDashColorII } ifelse
    lineto stroke
    /cnt cnt 1 add def
    grestore
    x1 y1 moveto
  } repeat
  x0 y0 x2 y2 ArrowB L pop pop%
}>
%
\def\nclineII{\pst@object{nclineII}}%
\def\nclineII@i{\check@arrow{\nclineII@ii}}%
\def\nclineII@ii#1#2{\nc@object{Open}{#1}{#2}{.5}%
    {\tx@NCLineII /LPutPos { xB yB xA yA \tx@LPutLine } def}%
}%
\def\pclineII{\pst@object{pclineII}}%
\def\pclineII@i{\pc@object\nclineII@ii}%
%
\define@key[psset]{}{lineAngle}{\psset{armB=0.5}\def\psk@lineAngle{#1}}%
%\psset{lineAngle=0}%
%
\pst@def{NCDiag}<{
  GetEdgeA GetEdgeB GetArmA GetArmB mark
  \psk@lineAngle\space abs 0 gt {
    /xTemp xA2 10 add def
    /yTemp yA2 \psk@lineAngle\space dup sin exch cos div 10 mul add def
    /dY1 yTemp yA2 sub def
    /dX1 xTemp xA2 sub def
    /dY2 yB2 yB1 sub def
    /dX2 xB2 xB1 sub def
    dX1 abs 0.01 lt {
      /m2 dY2 dX2 div def
      /xB2 xA2 def
      /yB2 xA2 xB1 sub m2 mul yB1 add def
    }{
      dX2 abs 0.01 lt {
        /m1 dY1 dX1 div def
        /xB2 xB1 def
        /yB2 xB1 xA2 sub m1 mul yA2 add def
      }{%
        /m1 dY1 dX1 div def
        /m2 dY2 dX2 div def
        /xB2 m1 xA2 mul m2 xB1 mul sub yA2 sub yB1 add m1 m2 sub div def
        /yB2 xB2 xA2 sub m1 mul yA2 add def
      } ifelse
    } ifelse
  } if
  ArmB 0 ne { xB1 yB1 } if
  xB2 yB2
  xA2 yA2
  ArmA 0 ne { xA1 yA1 } if
  tx@Dict begin false Line end
  /LPutVar [ xB1 yB1 xB2 yB2 xA2 yA2 xA1 yA1 ] cvx def
  /LPutPos { LPutLines } def
  /HPutPos { HPutLines } def
  /VPutPos { VPutLines } def
}>
% hv 2003-12-22
\pst@def{NCDiagg}<{
  GetEdgeA GetArmA \psk@lineAngle\space abs 0 gt { \psk@lineAngle\space }
    { yB yA2 sub xB xA2 sub Atan 180 add } ifelse /AngleB ED
  GetEdgeB mark
  \psk@lineAngle\space abs 0 gt {
    /dY2 yA2 yA1 sub def
    /dX2 xA2 xA1 sub def
    \psk@lineAngle\space abs 90 eq {
      /m2 dY2 dX2 div def
      /yA2 xB xA2 sub m2 mul yA2 add def
      /xA2 xB def
    }{
      /m1 \psk@lineAngle\space dup sin exch cos div def % tan alpha
      dX2 abs 0.01 lt {
        /yA2 xA1 xB sub m1 mul yB add def
        /xA2 xA1 def
      }{%
        /m2 dY2 dX2 div def
        /xA2 m1 xB mul m2 xA2 mul sub yA2 add yB sub m1 m2 sub div def
        /yA2 xA2 xB sub m1 mul yB add def
      } ifelse
    } ifelse
  } if
  xB1 yB1 xA2 yA2
  ArmA 0 ne { xA1 yA1 } if
  tx@Dict begin false Line end
  /LPutVar [ xB1 yB1 xA2 yA2 xA1 yA1 ] cvx def
  /LPutPos { LPutLines } def
  /HPutPos { HPutLines } def
  /VPutPos { VPutLines } def
}>
%
\def\ncbarr{\pst@object{ncbarr}}
\def\ncbarr@i#1#2{
  \begingroup
  \use@par%
  \psLNode(#1)(#2){0.5}{barr@tempNode}%
  \pst@dimm=\psk@angleA pt
  \pst@dimn=180pt
  % be sure, that angleA is 0 or 180. if not, we set it to 0
  \ifdim\pst@dimm=\z@\else\ifdim\pst@dimm=\pst@dimn\else\psset{angleA=0}\fi\fi
  \ncbar[arrows=-]{#1}{barr@tempNode}
  \ifdim\psk@angleA pt=\z@\relax
    \ncbar[angleA=180,angleB=180]{barr@tempNode}{#2}
  \else\ncbar[angleA=0,angleB=0]{barr@tempNode}{#2}\fi%
  \endgroup
}
%   #1-------#4----------------#2
% where #1#4= #3 * #1#2
%
\def\psLNode(#1)(#2)#3#4{%
  \pst@getcoor{#1}\pst@tempA%
  \pst@getcoor{#2}\pst@tempB%
  \pnode(!%
    \pst@tempA /YA exch \pst@number\psyunit div def
    /XA exch \pst@number\psxunit div def
    \pst@tempB /YB exch \pst@number\psyunit div def
    /XB exch \pst@number\psxunit div def
    /dx XB XA sub def
    /dy YB YA sub def
    XA dx #3\space mul add YA dy #3\space mul add){#4}
}
%
% build the linear combination #2*#1+#4*#3=#5
\def\psLCNode(#1)#2(#3)#4#5{%
  \pst@getcoor{#1}\pst@tempA%
  \pst@getcoor{#3}\pst@tempB%
  \pnode(!%
    \pst@tempA /YA exch \pst@number\psyunit div def
    /XA exch \pst@number\psxunit div def
    \pst@tempB /YB exch \pst@number\psyunit div def
    /XB exch \pst@number\psxunit div def
    XA #2\space mul XB #4\space mul add
    YA #2\space mul YB #4\space mul add){#5}%
}
%
\newif\ifPst@trueAngle
\define@key[psset]{}{trueAngle}[true]{\@nameuse{Pst@trueAngle#1}}
%\psset{trueAngle=false}
%
\def\psRelNode{\pst@object{psRelNode}}
\def\psRelNode@i(#1)(#2)#3#4{{% A - B - factor - node name
  \use@par
  \pst@getcoor{#1}\pst@tempA%
  \pst@getcoor{#2}\pst@tempB%
  \pnode(!
    \pst@tempA /YA exch \pst@number\psyunit div def
    /XA exch \pst@number\psxunit div def
    \pst@tempB /YB exch \pst@number\psyunit div def
    /XB exch \pst@number\psxunit div def
    /AlphaStrich \psk@angleA\space def
    /unit \pst@number\psyunit \pst@number\psxunit div def % yunit/xunit
%            
    /dx XB XA sub  def
    /dy YB YA sub \ifPst@trueAngle\space unit mul \fi\space def
    /laenge dy dup mul dx dup mul add sqrt #3 mul def
    /Alpha dy dx atan def 
    /beta Alpha AlphaStrich add def
    laenge beta cos mul XA add
    laenge beta sin mul \ifPst@trueAngle\space unit div \fi\space YA add ){#4}%
}}
%
\def\psRelLine{\pst@object{psRelLine}}
\def\psRelLine@i{\@ifnextchar({\psRelLine@iii}{\psRelLine@ii}}
\def\psRelLine@ii#1{%
  \addto@par{arrows=#1}%
  \psRelLine@iii%
}
\def\psRelLine@iii(#1)(#2)#3#4{{
  \pst@killglue
  \use@par
  \psRelNode(#1)(#2){#3}{#4}
  \psline(#1)(#4)%
}\ignorespaces}
%
% #1 options
% draw a parallel line to #2 #3
%     #2---------#3
%         #4----------#5(new node)
% #5 length of the line
% #6 node name
\def\psParallelLine{\pst@object{psParallelLine}}
\def\psParallelLine@i{\@ifnextchar({\psParallelLine@iii}{\psParallelLine@ii}}
\def\psParallelLine@ii#1{%
  \addto@par{arrows=#1}%
  \psParallelLine@iii%
}
\def\psParallelLine@iii(#1)(#2)(#3)#4#5{{
  \pst@killglue
  \use@par
  \pst@getcoor{#1}\pst@tempA
  \pst@getcoor{#2}\pst@tempB
  \pst@getcoor{#3}\pst@tempC
%  \pst@getlength{#4}\pst@dima
  \pnode(!%
     \pst@tempA /YA exch \pst@number\psyunit div def
     /XA exch \pst@number\psxunit div def
     \pst@tempB /YB exch \pst@number\psyunit div def
     /XB exch \pst@number\psxunit div def
     \pst@tempC /YC exch \pst@number\psyunit div def
     /XC exch \pst@number\psxunit div def
%            
    /dx XB XA sub  def
    /dy YB YA sub  def
    /laenge dy dup mul dx dup mul add sqrt #4 mul def
    /Alpha dy dx atan def 
    laenge Alpha cos mul XC add
    laenge Alpha sin mul YC add ){#5}%
  \psline(#3)(#5)
}\ignorespaces}
%
\def\psIntersectionPoint(#1)(#2)(#3)(#4)#5{%
    \pst@getcoor{#1}\pst@tempA
    \pst@getcoor{#2}\pst@tempB
    \pst@getcoor{#3}\pst@tempC
    \pst@getcoor{#4}\pst@tempd
\pnode(!%
     \pst@tempA /YA exch \pst@number\psyunit div def
     /XA exch \pst@number\psxunit div def
     \pst@tempB /YB exch \pst@number\psyunit div def
     /XB exch \pst@number\psxunit div def
     \pst@tempC /YC exch \pst@number\psyunit div def
     /XC exch \pst@number\psxunit div def
     \pst@tempd /YD exch \pst@number\psyunit div def
     /XD exch \pst@number\psxunit div def
    /dY1 YB YA sub def
    /dX1 XB XA sub def
    /dY2 YD YC sub def
    /dX2 XD XC sub def
    dX1 abs 0.01 lt {
        /m2 dY2 dX2 div def
        XA dup XC sub m2 mul YC add
    }{
        dX2 abs 0.01 lt {
            /m1 dY1 dX1 div def
            XC dup XA sub m1 mul YA add
        }{%
            /m1 dY1 dX1 div def
            /m2 dY2 dX2 div def
            m1 XA mul m2 XC mul sub YA sub YC add m1 m2 sub div dup
            XA sub m1 mul YA add
        } ifelse
    } ifelse ){#5}%
}
%
\def\psLDNode(#1)(#2)#3#4{%  
% #1: node A  #2: node B  #3: dimen measured from A  #4: node name
  \pst@getcoor{#1}\pst@tempA%
  \pst@getcoor{#2}\pst@tempB%
  \pssetlength\pst@dima{#3}%
  \pnode(!%
    \pst@tempA /YA exch \pst@number\psyunit div def
    /XA exch \pst@number\psxunit div def
    \pst@tempB /YB exch \pst@number\psyunit div def
    /XB exch \pst@number\psxunit div def
    /dx XB XA sub def
    /dy YB YA sub def
    /angle dy dx Atan def
    /length \pst@number\pst@dima \pst@number\psunit div def
    XA length angle cos mul add YA length angle sin mul add ){#4}%
}
\def\nlput{\pst@object{nlput}}
\def\nlput@i(#1)(#2)#3#4{%
  \begin@SpecialObj
  \psLDNode(A)(B){#3}{@temp@lnput}
  \pcline[linestyle=none](#1)(@temp@lnput)%
  \ncput[npos=1]{#4}%
  \end@SpecialObj
} %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%                                                  %%%%%%%%%%
%%%%%%%%%%%                pst-plot                          %%%%%%%%%%
%%%%%%%%%%%                                                  %%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\newif\ifPst@plot@comma
\define@key[psset]{}{comma}[true]{\@nameuse{Pst@plot@comma#1}}
%
\newif\ifPst@plot@xAxis
\newif\ifPst@plot@yAxis
\newif\ifPst@plot@xyAxes
\define@key[psset]{}{xAxis}[true]{\@nameuse{Pst@plot@xAxis#1}}
\define@key[psset]{}{yAxis}[true]{\@nameuse{Pst@plot@yAxis#1}}
\define@key[psset]{}{xyAxes}[true]{\@nameuse{Pst@plot@xAxis#1}\@nameuse{Pst@plot@yAxis#1}}%
%\psset{xyAxes=true}%
%
\define@key[psset]{}{xyDecimals}{\def\psk@xDecimals{#1}\def\psk@yDecimals{#1}}
\define@key[psset]{}{xDecimals}{\def\psk@xDecimals{#1}}
\define@key[psset]{}{yDecimals}{\def\psk@yDecimals{#1}}
%\psset{xyDecimals={}}%
%
\define@key[psset]{}{xlogBase}{\def\psk@xlogBase{#1}}
\define@key[psset]{}{ylogBase}{\def\psk@ylogBase{#1}}
\define@key[psset]{}{xylogBase}{\def\psk@xlogBase{#1}\def\psk@ylogBase{#1}}%
%\psset{xylogBase={}}%
%
\newif\ifPst@trigLabels
\define@key[psset]{pstricks-add}{trigLabels}[true]{%
  \@nameuse{Pst@trigLabels#1}%
  \ifPst@trigLabels
    \def\pst@@@hlabel##1{\pshlabel{##1}}
    \def\pshlabel##1{$%
      \ifnum##1=0 0\else%                        % ##1=0, print 0 and return 
        \def\pst@sign{\ifnum##1<0 -\fi}
        \pst@abs{##1}\pst@cnta
        \pst@mod{\pst@cnta}{2}\pst@cntc          % pst@cntc-> 0 or 1 (fraction or not)
        \ifnum1>\pst@cntc                        % 0: ##1\pi  1: ##1/2 \pi
          \pst@cntb=\pst@cnta \divide\pst@cntb by 2     % ##1/2
          \pst@sign\ifnum\pst@cntb>1 \the\pst@cntb\fi\pi % n*pi
        \else\pst@sign\frac{\ifnum\pst@cnta>1 \the\pst@cnta \fi\pi}{2}\fi
      \fi$}%                  n/2*pi
  \else
    \def\pst@@@hlabel##1{%
      \edef\@xyDecimals{\psk@xDecimals}%
      \ifnum\psk@ticks<\tw@ % ticks=all|x
        \ifx\psk@xlogBase\@empty
          \pshlabel{\expandafter\@LabelComma##1..\@nil\psk@xlabelFactor}%
        \else%
          \pshlabel{\psk@xlogBase\textsuperscript{\expandafter\@stripDecimals##1..\@nil }}
        \fi%
      \fi%
    }
    \def\pshlabel##1{$##1$}%
  \fi
}
%\psset[pstricks-add]{trigLabels=false}
%
%logLines=all|x|y|none  (0,1,2,3)
\define@key[psset]{}{logLines}{\pst@expandafter\psset@@logLines{#1}\@nil\psk@logLines}
\def\psset@@logLines#1#2\@nil#3{%
  \ifx#1a\let#3\z@\else
    \ifx#1x\let#3\@ne\else
      \ifx#1y\let#3\tw@\else
        \ifx#1n\let#3\thr@@\else
          \@pstrickserr{Bad argument: `#1#2'}\@ehpa
  \fi\fi\fi\fi}
%\psset{logLines=none}%
%
% Define "ticklines" parameter (ticklines=all|x|y|none with default=none)
%\def\psset@ticklines#1{\pst@expandafter\psset@@ticklines{#1}\@nil\psk@ticklines}
%\psset@ticklines{none}
\define@key[psset]{}{ylabelFactor}{\def\psk@ylabelFactor{#1}}
\define@key[psset]{}{xlabelFactor}{\def\psk@xlabelFactor{#1}}
%\psset{xlabelFactor=\relax,ylabelFactor=\relax}%
% The parameter styles for the tick lines
% (default=arrows=-,linestyle=dotted,dotsep=5pt)
%\newpsstyle{ticklinesXStyle}{arrows=-,linestyle=dotted,dotsep=5pt}
%\newpsstyle{ticklinesYStyle}{arrows=-,linestyle=dotted,dotsep=5pt}
%
%
%% #1 integer
%% #2 decimals
%% #3 dot
\def\@stripDecimals#1.#2.#3\@nil{%
  \def\dummy{#1}%
  \ifx\dummy\@empty\the\@zero\else#1\fi% the integer part
}
%
\def\pst@@@vlabel#1{%
  \edef\@xyDecimals{\psk@yDecimals}%
%  \psk@yLabel%
  \ifodd\psk@ticks  % ticks=all||y (0,2)
  \else
    \ifx\psk@ylogBase\@empty
%      \ifPst@plot@comma
       \psvlabel{\expandafter\@LabelComma#1..\@nil\psk@ylabelFactor}%
%      \else\psvlabel{#1\psk@ylabelFactor}\fi%
    \else%
      \psvlabel{\psk@ylogBase\textsuperscript{\expandafter\@stripDecimals#1..\@nil }}
    \fi%
  \fi%
}
\newcount\@digitcounter\@digitcounter=0\relax
\def\@inc@digitcounter{\global\advance\@digitcounter by 1\relax}
\def\@get@digitcounter{\the\@digitcounter\relax}
\def\@Reset@digitcounter{\global\@digitcounter=0\relax}
\def\@zeroFill{%
  \ifnum \@xyDecimals>\@get@digitcounter
    \bgroup
      0\@inc@digitcounter\@zeroFill
    \egroup%
  \fi%
}
% #1 the value, maybe empty
%
\def\@process@digits#1#2;{%
	\ifx *#1\@zeroFill\else#1\@inc@digitcounter\@process@digits#2;\fi%
}
\def\@writeDecimals#1{%
  \ifx\@xyDecimals\@empty% take value as is
    \def\@tempa{#1}% write only if not empty
    \ifx\@tempa\@empty% write nothing
    \else
      \ifPst@plot@comma{,}\else.\fi%
      #1%
    \fi%
  \else% write only \xy@decimals
    \ifnum\@xyDecimals>\@zero
      \ifPst@plot@comma{,}\else.\fi
        \@Reset@digitcounter
        \@process@digits#1*;
      \fi%
  \fi%
}
%% #1 integer
%% #2 decimals
%% #3 dot
\def\@LabelComma#1.#2.#3\@nil{%
  \def\pst@tempA{#1}%
  \ifx\pst@tempA\@empty\the\@zero\else#1\fi% the integer part
  \def\pst@tempA{#2}%
  \ifx\pst@tempA\@empty\@writeDecimals{}\else\@writeDecimals{#2}\fi%
}
%
\def\psxs@none{%
  \let\psk@arrowA\@empty%
  \let\psk@arrowB\@empty%
  \psxs@axes%
}
%\def\psxs@axes{%
%  \psxs@@axes\pst@dima\pst@dimc{}%
%  \psxs@@axes\pst@dimb\pst@dimd{exch}%
%}

%
\def\psxs@axes{{%
  \ifPst@plot@xAxis\psxs@@axes\pst@dima\pst@dimb\pst@dimc\pst@dimd{}\fi%
  \ifPst@plot@yAxis\psxs@@axes\pst@dima\pst@dimb\pst@dimc\pst@dimd{exch}\fi%
}}
\def\psaxes{\pst@object{psaxes}}
\def\psaxes@i{\pst@getarrows\psaxes@ii}
\def\psaxes@ii(#1){\@ifnextchar({\psaxes@iii(#1)}{\psaxes@iv(0,0)(0,0)(#1)}}
\def\psaxes@iii(#1)(#2){\@ifnextchar({\psaxes@iv(#1)(#2)}{\psaxes@iv(#1)(#1)(#2)}}
%
\def\psaxes@iv(#1,#2)(#3,#4)(#5,#6){%
  \pst@killglue%
  \begingroup%
  \setbox\pst@hbox=\hbox\bgroup%
  \use@par%
  \pssetxlength\pst@dimg{#1}% o-x
  \pssetylength\pst@dimh{#2}% o-y
  \pssetxlength\pst@dima{#3}% bl-x
  \pssetylength\pst@dimb{#4}% bl-y
  \pssetxlength\pst@dimc{#5}% ur-x
  \pssetylength\pst@dimd{#6}% ur-y
    % If minimum values are negative in log mode, we modify Ox
    % (respectively Oy) if this was not done by the user
    % X axis labels (\psk@log = 0 or 1)
%
% Whole thing will be translated to origin:
  \advance\pst@dima-\pst@dimg% Dist. from bl-x to o-x
  \advance\pst@dimb-\pst@dimh% Dist. from bl-y to o-y
  \advance\pst@dimc-\pst@dimg% Dist. from ur-x to o-x
  \advance\pst@dimd-\pst@dimh% Dist. from ur-y to o-y
% Make lines/arrows or frame:
  \@nameuse{psxs@\psk@axesstyle}%  \psxs@axes or \psxs@frame
  \ifPst@plot@yAxis%
  \begingroup%
    \ifdim\pst@dima=\z@\else\showoriginfalse\fi%
    \ifnum\psk@dy=\z@%
      \pst@dimg=\psk@Dy\psyunit%
      \edef\psk@dy{\number\pst@dimg}%
    \fi%
    \ifPst@plot@xAxis\else\showorigintrue\fi%
    \pst@vlabels{\pst@dimd}{\psk@arrowB}{#3}{#5}%
    \ifPst@plot@xAxis\showoriginfalse\fi%
    \pst@vlabels{\pst@dimb}{\psk@arrowA}{#3}{#5}%
  \endgroup%
  \fi%
  \ifPst@plot@xAxis%
  \begingroup%
    \ifdim\pst@dimb=\z@\else\showoriginfalse\fi%
    \ifnum\psk@dx=\z@%
      \pst@dimg=\psk@Dx\psxunit%
      \edef\psk@dx{\number\pst@dimg}%
    \fi%
    \ifPst@plot@yAxis\else\showorigintrue\fi%
    \pst@hlabels{\pst@dimc}{\psk@arrowB}{#4}{#6}%
    \ifPst@plot@yAxis\showoriginfalse\fi%
    \pst@hlabels{\pst@dima}{\psk@arrowA}{#4}{#6}%
  \endgroup%
  \fi%
% Now close "\pst@hbox" (which is 0-dimensional), and put it at the origin.
  \egroup%
  \pssetxlength\pst@dimg{#1}%
  \pssetylength\pst@dimh{#2}%
  \leavevmode\psput@cartesian\pst@hbox%
  \endgroup
  \ignorespaces%
}
%
\newdimen\psk@subticksize\psk@subticksize=\z@
\newdimen\pst@xticksizeA
\newdimen\pst@xticksizeB
\newdimen\pst@xticksizeC
\newdimen\pst@yticksizeA
\newdimen\pst@yticksizeB
\newdimen\pst@yticksizeC
%
\def\set@xticksize#1{%
  \pst@expandafter\pst@getydimdim{#1} {} {}\@nil % y-unit!!
  \pst@xticksizeA=\the\pst@dimm%
  \pst@xticksizeB=\the\pst@dimn%
  \edef\psk@xticksize{\pst@number\pst@xticksizeA \pst@number\pst@xticksizeB}%
  \ifdim\pst@dimm=\z@\relax
    \pst@xticksizeC=\z@
  \else%
    \pst@absdim{\pst@xticksizeA}\pst@dimm%
    \pst@absdim{\pst@xticksizeB}\pst@dimn%
    \pst@maxdim{\pst@dimm}{\pst@dimn}\pst@dimo%
    \pst@xticksizeC=\pst@dimo%
  \fi%
}
\def\set@yticksize#1{%
  \pst@expandafter\pst@getxdimdim{#1} {} {}\@nil % x-unit!
  \pst@yticksizeA=\the\pst@dimm%
  \pst@yticksizeB=\the\pst@dimn%
  \edef\psk@yticksize{\pst@number\pst@yticksizeA \pst@number\pst@yticksizeB}%
  \ifdim\pst@dimm=\z@\relax
    \pst@yticksizeC=\z@
  \else%
    \pst@absdim{\pst@yticksizeA}\pst@dimm%
    \pst@absdim{\pst@yticksizeB}\pst@dimn%
    \pst@maxdim{\pst@dimm}{\pst@dimn}\pst@dimo%
    \pst@yticksizeC=\pst@dimo%
  \fi%
}
\define@key[psset]{}{ticksize}{\set@xticksize{#1}\set@yticksize{#1}}
\define@key[psset]{}{xticksize}{\set@xticksize{#1}}
\define@key[psset]{}{yticksize}{\set@yticksize{#1}}%  overwrites the definition in pstricks
%\psset{ticksize=-4pt 4pt}
%
% full= 0, top=1, bottom=-1
\define@key[psset]{}{tickstyle}{%
  \pst@expandafter\psset@@tickstyle{#1}\@nil%
  \pst@cnta=\psk@tickstyle
  \advance\pst@cnta by 1
  \ifcase\pst@cnta% bottom
    \pst@xticksizeB=\z@
    \pst@yticksizeB=\z@
  \or% full
  \or% top
    \pst@xticksizeA=\z@
    \pst@yticksizeA=\z@
  \fi
}
%\psset{tickstyle=full}%
%
%
\define@key[psset]{}{subticks}{\def\psk@xsubticks{#1}\def\psk@ysubticks{#1}}
\define@key[psset]{}{xsubticks}{\def\psk@xsubticks{#1}}
\define@key[psset]{}{ysubticks}{\def\psk@ysubticks{#1}}
%
\define@key[psset]{}{subticksize}{\def\psk@xsubticksize{#1}\def\psk@ysubticksize{#1}}
\define@key[psset]{}{xsubticksize}{\def\psk@xsubticksize{#1}}
\define@key[psset]{}{ysubticksize}{\def\psk@ysubticksize{#1}}
%
\define@key[psset]{}{tickwidth}{%
  \pst@getlength{#1}\psk@xtickwidth%
  \pst@getlength{#1}\psk@ytickwidth}
\define@key[psset]{}{xtickwidth}{\pst@getlength{#1}\psk@xtickwidth}
\define@key[psset]{}{ytickwidth}{\pst@getlength{#1}\psk@ytickwidth}
\define@key[psset]{}{subtickwidth}{%
  \pst@getlength{#1}\psk@xsubtickwidth%
  \pst@getlength{#1}\psk@ysubtickwidth}
\define@key[psset]{}{xsubtickwidth}{\pst@getlength{#1}\psk@xsubtickwidth}
\define@key[psset]{}{ysubtickwidth}{\pst@getlength{#1}\psk@ysubtickwidth}
%
\define@key[psset]{}{tickcolor}{\def\psk@xtickcolor{#1}\def\psk@ytickcolor{#1}}
\define@key[psset]{}{xtickcolor}{\def\psk@xtickcolor{#1}}
\define@key[psset]{}{ytickcolor}{\def\psk@ytickcolor{#1}}
\define@key[psset]{}{subtickcolor}{%
  \pst@getcolor{#1}\psk@xsubtickcolor%
  \pst@getcolor{#1}\psk@ysubtickcolor}
\define@key[psset]{}{xsubtickcolor}{\pst@getcolor{#1}\psk@xsubtickcolor}
\define@key[psset]{}{ysubtickcolor}{\pst@getcolor{#1}\psk@ysubtickcolor}
%
\define@key[psset]{}{xticklinestyle}{%
  \@ifundefined{psls@#1}%
    {\@pstrickserr{Line style `#1' not defined}\@eha}%
    {\def\psxticklinestyle{#1}}}
\define@key[psset]{}{xsubticklinestyle}{%
  \@ifundefined{psls@#1}%
    {\@pstrickserr{Line style `#1' not defined}\@eha}%
    {\def\psxsubticklinestyle{#1}}}
\define@key[psset]{}{yticklinestyle}{%
  \@ifundefined{psls@#1}%
    {\@pstrickserr{Line style `#1' not defined}\@eha}%
    {\def\psyticklinestyle{#1}}}
\define@key[psset]{}{ysubticklinestyle}{%
  \@ifundefined{psls@#1}%
    {\@pstrickserr{Line style `#1' not defined}\@eha}%
    {\def\psysubticklinestyle{#1}}}
\define@key[psset]{}{ticklinestyle}{%
  \@ifundefined{psls@#1}%
    {\@pstrickserr{Line style `#1' not defined}\@eha}%
    {\def\psxticklinestyle{#1}\def\psyticklinestyle{#1}}}
\define@key[psset]{}{subticklinestyle}{%
  \@ifundefined{psls@#1}%
    {\@pstrickserr{Line style `#1' not defined}\@eha}%
    {\def\psxsubticklinestyle{#1}\def\psysubticklinestyle{#1}}}
%
\define@key[psset]{}{ticklinestyle}{\psset{xticklinestyle=#1,yticklinestyle=#1}}
\define@key[psset]{}{subticklinestyle}{\psset{xsubticklinestyle=#1,ysubticklinestyle=#1}}
%\psset{subticksize=0.75,subticks=1,tickcolor=black,ticklinestyle=solid,%
%  subticklinestyle=solid,%
%  subtickcolor=gray,%
%  tickwidth=0.5\pslinewidth,%
%  subtickwidth=0.25\pslinewidth}
%
\newif\ifis@yAxis%
%
\def\psxs@@axes#1#2#3#4#5{% llx,lly,urx,ury,exch,arrowA,arrowB
  \pst@killglue%
  \begin@SpecialObj%
    \def\pst@tempA{#5}%
    \ifx\pst@tempA\@empty\relax%
      \is@yAxisfalse%
      \ifnum\psk@dx=\z@%
        \pst@dimg=\psk@Dx\psxunit%
        \def\psk@dx{\number\pst@dimg}%
      \fi%
    \else%
      \is@yAxistrue%
      \ifnum\psk@dy=\z@%
        \pst@dimg=\psk@Dy\psyunit% 
        \def\psk@dy{\number\pst@dimg}%
      \fi%
    \fi% 
    \let\pst@linetype\pst@arrowtype%
    \def\pst@tempA{none}%
    \pst@addarrowdef%
    \addto@pscode{
      \ifis@yAxis 0 \pst@number#4 \else \pst@number#3 0 \fi
      \ifis@yAxis 0 \pst@number#2 \else \pst@number#1 0 \fi
      ArrowA
      CP 4 2 roll
      ArrowB 
      /yEnd exch def /xEnd exch def
      xEnd yEnd 
      \ifx\psk@axesstyle\pst@tempA
        pop pop % axesstyle = none (only ticks)
      \else
        L                                  % the line with arrows 
      \fi
      /yStart exch def
      /xStart exch def
      \@nameuse{psls@\pslinestyle}                 % linestyle for the axes
      stroke                                       % draw the main line
%     \psk@ticks: all=0; x=1; y=2; none=3
      \number\psk@ticks\space dup 2 mod 0 eq \ifis@yAxis true \else false \fi and 
      exch 2 lt \ifis@yAxis false \else true \fi and or {
      /viceversa 
        \ifis@yAxis\pst@number#2 \pst@number#4 \else\pst@number#1 \pst@number#3 \fi
         gt { true }{ false } ifelse def           % other way round
      /epsilon 0.01 def                            % rounding errors
      /minTickline \ifis@yAxis \pst@number#1 \else \pst@number#2 \fi def
      /maxTickline \ifis@yAxis \pst@number#3 \else \pst@number#4 \fi def
      /dT \ifis@yAxis\psk@dy\else\psk@dx\fi\space 65536 div viceversa {neg} if def 
      /subTNo \ifis@yAxis\psk@ysubticks\else\psk@xsubticks\fi \space def
      subTNo 0 gt { /dsubT dT subTNo div def}{ /dsubT 0 def } ifelse  % deltaSubTick
      \ifis@yAxis \psk@yticksize \else \psk@xticksize \fi
      /tickend exch def /tickstart exch def
      /Twidth \ifis@yAxis \psk@ytickwidth \else \psk@xtickwidth \fi\space def
      /subTwidth \ifis@yAxis \psk@ysubtickwidth \else \psk@xsubtickwidth \fi\space def
      /STsize \ifis@yAxis \psk@ysubticksize \else \psk@xsubticksize \fi\space def
      /TColor {
        \ifis@yAxis\pst@usecolor\psk@ytickcolor
        \else\pst@usecolor\psk@xtickcolor\fi\space } def
      /subTColor {
        \ifis@yAxis\pst@usecolor\psk@ysubtickcolor
        \else\pst@usecolor\psk@xsubtickcolor\fi\space } def
      /MinValue { \ifis@yAxis yStart \else xStart \fi
        \ifx\psk@arrowA\@empty\else 
          \psk@arrowsize\space CLW mul add \psk@arrowlength\space mul 
           viceversa { sub epsilon add } { add epsilon sub } ifelse \fi } def
      /MaxValue { \ifis@yAxis yEnd \else xEnd \fi
        \ifx\psk@arrowB\@empty\else
          \psk@arrowsize\space CLW mul add \psk@arrowlength\space mul 
           viceversa { add epsilon sub } { sub epsilon add } ifelse \fi } def
      /logLines {
        \ifnum\psk@logLines=\z@ true \else         % all axes
          \ifnum\psk@logLines<\tw@                 % x axis
            \ifis@yAxis false \else true \fi       % do we have x or y axis
          \else
            \ifnum\psk@logLines<\thr@@             % y axis
              \ifis@yAxis true \else false \fi     % do we have x or y axis
            \else 
              false                                % no one
            \fi
          \fi
        \fi
      } def
      /LSstroke {                                  % set linestyle and stroke
        \ifis@yAxis\@nameuse{psls@\psyticklinestyle}
        \else\@nameuse{psls@\psxticklinestyle}\fi } def
      /subLSstroke {                               % set sublinestyle and stroke
        \ifis@yAxis\@nameuse{psls@\psysubticklinestyle}
        \else\@nameuse{psls@\psxsubticklinestyle}\fi } def
%\iffalse
% start ticks ---------------------------------------------------------
      0 dT MaxValue {                              % the positive part of the axes
        /cntTick exch def                          % the index
        logLines {                                 % log lines?
          gsave
          1 10 subTNo div 9.99 {                   % do not write a line for 1
            /dx exch def                           % save index
            /x cntTick dT dx log mul add def       %
            x abs MaxValue abs le {                % out of range?
              x minTickline #5\space moveto
              x maxTickline #5\space lineto
            } if
          } for
          subTwidth SLW subTColor                  % set line width and subtick color
          subLSstroke
          grestore                                 % restore main tick status
          stroke
          /dsubT 0 def                             % no other subticks
        } if
        dsubT abs 0 gt {                           % du we have subticks?
          gsave                                    % save graphic state
% start subticks ----------------------------------------------------------
            /cntsubTick cntTick dsubT add def
            subTNo 1 sub {
            cntsubTick abs MaxValue abs le {       % out of range?
              cntsubTick tickstart STsize mul #5\space moveto
              cntsubTick tickend STsize mul #5\space lineto
            }{ exit }  ifelse
            /cntsubTick cntsubTick dsubT add def
          } repeat 
          subTwidth SLW subTColor                  % set line width and subtick color
          subLSstroke
% end subticks ----------------------------------------------------------
          grestore                                 % restore tick status
        } if
        gsave
        cntTick tickstart #5\space moveto          % line begin main Tick
        cntTick tickend #5\space lineto            % lineto tick end
        Twidth SLW TColor                          % set line width and tick color
        LSstroke
        grestore
      } for
% end ticks ----------------------------------------------------------
%\fi
%\iffalse
% ================================================ % the other side 
      /dT dT neg def                               % the other side of the axis
      /dsubT dsubT neg def
% start ticks ----------------------------------------------------------
      0 dT MinValue epsilon viceversa { add }{ sub } ifelse {
        /cntTick exch def
        logLines {                                 % log lines?
          gsave
          1 10 subTNo div 9.99 {                   % do not write a line for 1
            /dx exch def                           % save index
            /x cntTick dT dx log mul add def       %
            x abs MinValue abs le {                % out of range?
              x minTickline #5\space moveto
              x maxTickline #5\space lineto
            } if
          } for
          /dsubT 0 def 
          subTwidth SLW subTColor                  % set line width and subtick color
          subLSstroke
          grestore
        }
        dsubT abs 0 gt {                           % do we have subticks?
          gsave                                    % save main state
% start subticks ----------------------------------------------------------
          /cntsubTick cntTick dsubT add def
          subTNo 1 sub {
            cntsubTick abs MinValue abs le {       % out of range?
              cntsubTick tickstart STsize mul #5\space moveto
              cntsubTick tickend STsize mul #5\space lineto
            }{ exit } ifelse
            /cntsubTick cntsubTick dsubT add def
          } repeat % for
% end subticks ----------------------------------------------------------
          subTwidth SLW subTColor                  % set line width and subtick color
          subLSstroke
          grestore                                 % restore main state
        } if
        gsave
        cntTick tickstart #5\space moveto         % line begin main Tick
        cntTick tickend #5\space lineto           % lineto tick end
        Twidth SLW TColor                         % set line width and tick color
        LSstroke
        grestore
      } for
% end ticks ----------------------------------------------------------
%\fi    
    } if%
   }%  
  \end@SpecialObj%
  \ignorespaces%
}%
%
\def\psxs@frame{%
  \begin@SpecialObj%
    \addto@pscode{%
      \pst@number\pst@dima \pst@number\pst@dimb moveto \pst@number\pst@dimc \pst@number\pst@dimb L
      \pst@number\pst@dimc \pst@number\pst@dimd L \pst@number\pst@dima \pst@number\pst@dimd L 
      closepath}%
    \pst@stroke%
    \psk@fillstyle%
  \end@SpecialObj%
  \let\psk@arrowA\@empty%
  \let\psk@arrowB\@empty%
%  \pst@dima=0pt\pst@dimb=0pt%
%  \psset{xticksize=0 \pst@dimd,yticksize=0 \pst@dimc}%
  \pst@xticksizeC=\z@\pst@yticksizeC=\z@%
  \psxs@@axes\pst@dima\pst@dimb\pst@dimc\pst@dimd{}%
  \psxs@@axes\pst@dima\pst@dimb\pst@dimc\pst@dimd{exch}%
}
%
% #1:Max/Min in pt from origin; #2:arrow; #3:min; #4:max
\def\pst@hlabels#1#2#3#4{%
  \ifdim#1=\z@\else%                   % start from 0 ?
    \ifx#2\empty\else\advance#1\ifdim#1>\z@-\fi7\pslinewidth\fi%
    \pst@cnta=#1\relax%                % Distance (in sp) to end.
    \divide\pst@cnta\psk@dx\relax%     % Number of ticks/labels
    \ifnum\pst@cnta=\z@\else%
      \pst@dimb=\psk@dx sp%            % Space between ticks.
%        \ifPst@plot@yAxis\else\showorigintrue\fi%
        \ifnum\psk@labels<\tw@ \ifPst@plot@xAxis\pst@@hlabels\fi\fi%
        \showoriginfalse%
    \fi%
  \fi%
}
% Knows \pst@dimb and \pst@cnta
\def\pst@@hlabels{%
  \pst@dimm=\pst@xticksizeC\advance\pst@dimm by \pslabelsep%
  \vbox to\z@{%
    \ifdim\pst@dimd>\z@\vskip\pst@dimm\else\vss\fi%
    \ifnum\pst@cnta<\z@\pst@dimb=-\pst@dimb\fi%
    \hbox to\z@{%
      \ifshoworigin\hbox to \z@{\hss\pst@@@hlabel{\psk@Ox}\hss}\fi%
      \mmultido{\n=\psk@Ox+\psk@Dx}{\pst@cnta}{%
        \hskip\pst@dimb\hbox to \z@{\hss\pst@@@hlabel{\n}\hss}%
      }\hss%
    }%
    \ifdim\pst@dimd>\z@\vss\else\vskip\pst@dimm\fi%
}}%

% #1:Max/Min in pt from origin; #2:arrow; #3:min; #4:max
% \psk@labels 0:all; 1:x; 2:y; 3:none
\def\pst@vlabels#1#2#3#4{%
  \ifdim#1=\z@\else%
    \ifx#2\empty\else\advance#1\ifdim#1>\z@-\fi7\pslinewidth\fi%
    \pst@cnta=#1\relax          %      % Distance (in sp) to end.
    \divide\pst@cnta\psk@dy\relax  %   % Number of ticks/labels
    \ifnum\pst@cnta=\z@\else%
      \pst@dima=\psk@dy sp%            % Space between ticks.
%      \ifPst@plot@xAxis\else\showorigintrue\fi%
      \ifodd\number\psk@labels\else\ifPst@plot@yAxis\pst@@vlabels\fi\fi%
      \showoriginfalse%
    \fi%
  \fi%
}
% \pst@dima: the width between two labels in pt
% \pst@dimc: the coordinate of the origin in pt
% \pst@cnta: the lowest label
\def\pst@@vlabels{%
  \pst@dimm=\pst@yticksizeC%
  \advance\pst@dimm by \pslabelsep%
  \vbox to\z@{%
    \ifnum\pst@cnta>\z@\pst@dima=-\pst@dima\fi%
    \offinterlineskip%
    \ifshoworigin
      \vbox to \z@{\vss\hbox to\z@{%
        \ifdim\pst@dimc>\z@\hss\else\hskip\pst@dimm\fi
        \pst@@@vlabel{\psk@Oy}%
        \ifdim\pst@dimc>\z@\hskip\pst@dimm\else\hss\fi}\vss}%
    \fi%
    \mmultido{\n=\psk@Oy+\psk@Dy}{\pst@cnta}{%
      \vbox to\pst@dima{\vss}
      \vbox to \z@{%
        \vss\hbox to\z@{%
          \ifdim\pst@dimc>\z@%
            \hss\pst@@@vlabel{\n}\hskip\pst@dimm%
          \else%
            \hskip\pst@dimm\pst@@@vlabel{\n}\hss%
          \fi
        }\vss%
    }}%
    \vss%
}}
%
\define@key[psset]{}{nStep}{\def\psk@nStep{#1}}
\define@key[psset]{}{nStart}{\def\psk@nStart{#1}}
\define@key[psset]{}{nEnd}{\def\psk@nEnd{#1}}
\define@key[psset]{}{xStep}{\def\psk@xStep{#1}}
\define@key[psset]{}{yStep}{\def\psk@yStep{#1}}
%
\define@key[psset]{}{xStart}{\def\psk@xStart{#1}}
\define@key[psset]{}{xEnd}{\def\psk@xEnd{#1}}
\define@key[psset]{}{yStart}{\def\psk@yStart{#1}}
\define@key[psset]{}{yEnd}{\def\psk@yEnd{#1}}
%
\define@key[psset]{}{plotNo}{\def\psk@plotNo{#1}}
\define@key[psset]{}{plotNoMax}{\def\psk@plotNoMax{#1}}
%
%\psset{nStep=1, nStart=0, nEnd={},%
%  xStep=0, yStep=0, xStart={}, xEnd={},  yStart={}, yEnd={}, comma=false,%
%  plotNo=1,plotNoMax=1}%
%
\def\pstScalePoints(#1,#2)#3#4{%
%  xScale | yScale | xOperator | yOperator  
% the operators can be any Postscript code
  \pst@def{ScalePoints}<%
    /y ED /x ED
    counttomark dup dup cvi eq not { exch pop } if
    /m exch def /n m 2 div cvi def
    n {
      #4\space y mul #2\space mul m 1 roll
      #3\space x mul #1\space mul m 1 roll
      /m m 2 sub
      def } repeat>
}
%\pstScalePoints(1,1){}{}% the default -> no special operators
%
\def\listplot@ii#1{%
  \@nameuse{beginplot@\psplotstyle}%
  \addto@pscode{/D {} def mark}%
  #1%
  \addto@pscode{%
    \tx@PreparePoints
    \pst@number\psxunit
    \pst@number\psyunit
    \tx@ScalePoints%
  }%
  \@nameuse{endplot@\psplotstyle}%
}
%
\newif\ifPst@ChangeOrder
\define@key[psset]{}{ChangeOrder}[true]{\@nameuse{Pst@ChangeOrder#1}}
\pst@def{PreparePoints}<{%
  counttomark /m exch def
  \ifPst@ChangeOrder
    /m0 m def
    m \psk@plotNoMax\space 1 add div 1 sub cvi {
      m0 \psk@plotNoMax\space 1 add roll /m0 m0 \psk@plotNoMax\space 1 add sub def
    } repeat
  \fi
  /n m \psk@plotNoMax\space 1 add div cvi def
  \psk@plotNoMax\space 1 gt {% multiple data files?
    n {
      \psk@plotNoMax\space \psk@plotNo\space 1 sub neg roll % x yNo y y y ...
      \psk@plotNoMax\space 1 sub { pop } repeat % x yNo
      /m m \psk@plotNoMax\space 1 sub sub def
      m 2 roll
    } repeat
  } if % no multiple data files
%	counttomark /m exch def
%	/n m 2 div cvi def
  /xMax -99999 def /yMax -99999 def
  /xP 0 def /yP 0 def
  m copy
  n {
    /y exch def /x exch def
    xMax x lt { /xMax x def } if
    yMax y lt {/yMax y def } if
    xP x gt { /xP x def } if
    yP y gt { /yP y def } if
  } repeat
%	m 2 roll
  \psk@xStep\space 0 gt \psk@yStep\space 0 gt or (\psk@xStart) length 0 gt or
  (\psk@yStart) length 0 gt or (\psk@xEnd) length 0 gt or (\psk@yEnd) length 0 gt or {
%
    (\psk@xStart) length 0 gt {\psk@xStart\space }{ xP } ifelse /xStart exch def
    (\psk@yStart) length 0 gt {\psk@yStart\space }{ yP } ifelse /yStart exch def
    (\psk@xEnd) length 0 gt { \psk@xEnd\space }{ xMax } ifelse /xEnd exch def
    (\psk@yEnd) length 0 gt { \psk@yEnd\space }{ yMax } ifelse /yEnd exch def
    n {
      m -2 roll
      2 copy /yVal exch def /xVal exch def
      xVal xP ge
      yVal yP ge and
      xVal xEnd le and
      yVal yEnd le and
      xVal xStart ge and
      yVal yStart ge and {
        /xP xP \psk@xStep\space add def
        /yP yP \psk@yStep\space add def
      }{%
        pop pop
        /m m 2 sub def
      } ifelse
    } repeat
  }{%
    /ncount 0 def
    (\psk@nEnd) length 0 gt { \psk@nEnd\space }{ m } ifelse 
    /nEnd exch def
    n {
      m -2 roll
      \psk@nStep\space 1 gt {
        ncount \psk@nStart\space sub \psk@nStep\space mod 0 eq }{ true } ifelse
        ncount nEnd le and
        ncount \psk@nStart\space ge and not {
          pop pop
          /m m 2 sub def
        } if
        /ncount ncount 1 add def
      } repeat
  } ifelse
}>
%
%
\define@key[psset]{}{xAxisLabel}{\def\psk@xAxisLabel{#1}}
\define@key[psset]{}{yAxisLabel}{\def\psk@yAxisLabel{#1}}
%\psset{xAxisLabel=x,yAxisLabel=y}
\define@key[psset]{}{xAxisLabelPos}{\def\psk@xAxisLabelPos{#1}}
\define@key[psset]{}{yAxisLabelPos}{\def\psk@yAxisLabelPos{#1}}
%\psset{yAxisLabelPos={},xAxisLabelPos={}}
%
\newdimen\psk@llx
\newdimen\psk@lly
\newdimen\psk@urx
\newdimen\psk@ury
\define@key[psset]{}{llx}{\pssetxlength\psk@llx{#1}}
\define@key[psset]{}{lly}{\pssetylength\psk@lly{#1}}
\define@key[psset]{}{urx}{\pssetxlength\psk@urx{#1}}
\define@key[psset]{}{ury}{\pssetylength\psk@ury{#1}}
%\psset{llx=\z@, lly=\z@, urx=\z@, ury=\z@}% prevents rounding errors 
\newif\ifPst@plot@box
\define@key[psset]{}{box}[true]{\@nameuse{Pst@plot@box#1}}
%
\newdimen\pst@xunit
\newdimen\pst@yunit
%
\def\psgraph{\def\pst@par{}\pst@object{psgraph}}
\def\psgraph@i{\pst@getarrows\psgraph@ii}
\def\psgraph@ii(#1,#2){\@ifnextchar({\psgraph@iii(#1,#2)}{\psgraph@iv(0,0)(#1,#2)}}
\def\psgraph@iii(#1,#2)(#3,#4){\@ifnextchar({\psgraph@v(#1,#2)(#3,#4)}{\psgraph@iv(#1,#2)(#3,#4)}}
%
\def\psgraph@iv(#1,#2)(#3,#4)#5#6{%  no special origin defined
% minX | minY | maxX | maxY | Length x-axis | length y-axis%  
  \pst@killglue
  \begingroup
  \pst@dimo=#3\p@\advance\pst@dimo by -#1\p@ % delta x
  \pst@divide{#5}{\pst@dimo}\pst@tempA
  \pst@xunit=\pst@tempA\p@%
  \pst@dimo=#4\p@\advance\pst@dimo by -#2\p@ % delta y
  \pst@dima=#6
  \pst@divide\pst@dima{\pst@dimo}\pst@tempA%
  \pst@yunit=\pst@tempA\p@%
  %
  \pst@dima=#1\pst@xunit \advance\pst@dima by \psk@llx%
  \pst@dimb=#2\pst@yunit \advance\pst@dimb by \psk@lly%
  \pst@dimc=#3\pst@xunit \advance\pst@dimc by \psk@urx%
  \pst@dimd=#4\pst@yunit \advance\pst@dimd by \psk@ury%
  \if@star\pspicture*(\pst@dima,\pst@dimb)(\pst@dimc,\pst@dimd)\else
    \pspicture(\pst@dima,\pst@dimb)(\pst@dimc,\pst@dimd)\fi
  \psset{xunit=\pst@xunit,yunit=\pst@yunit}%
  \bgroup
  \use@par
  \psaxes(#1,#2)(#3,#4)
  \egroup
  \psgraph@vi(#1,#2)(#3,#4)%
}
\def\psgraph@v(#1,#2)(#3,#4)(#5,#6)#7#8{%  with special origin
% Xorig | yorig | minX | minY | maxX | maxY | Length x-axis | length y-axis%  
  \pst@killglue
  \begingroup
  \pst@dimo=#5\p@\advance\pst@dimo by -#3\p@ % delta x
  \pst@divide{#7}{\pst@dimo}\pst@tempA
  \pst@xunit=\pst@tempA\p@%
  \pst@dimo=#6\p@\advance\pst@dimo by -#4\p@ % delta y
  \pst@dima=#8
  \pst@divide\pst@dima{\pst@dimo}\pst@tempA%
  \pst@yunit=\pst@tempA\p@%
  %
  \pst@dima=#3\pst@xunit \advance\pst@dima by \psk@llx%
  \pst@dimb=#4\pst@yunit \advance\pst@dimb by \psk@lly%
  \pst@dimc=#5\pst@xunit \advance\pst@dimc by \psk@urx%
  \pst@dimd=#6\pst@yunit \advance\pst@dimd by \psk@ury%
  \if@star\pspicture*(\pst@dima,\pst@dimb)(\pst@dimc,\pst@dimd)\else
    \pspicture(\pst@dima,\pst@dimb)(\pst@dimc,\pst@dimd)\fi
  \psset{xunit=\pst@xunit,yunit=\pst@yunit}%
  \bgroup
  \use@par
  \psaxes(#1,#2)(#3,#4)(#5,#6)
  \egroup
  \psgraph@vi(#1,#2)(#5,#6)%
}
\def\psgraph@vi(#1,#2)(#3,#4){%
  \ifx\psk@xAxisLabel\@empty\else%
    \ifx\psk@xAxisLabelPos\@empty\uput[0](#3,#2){\psk@xAxisLabel}%
    \else\rput(\psk@xAxisLabelPos){\psk@xAxisLabel}%
    \fi%
  \fi%
  \ifx\psk@yAxisLabel\@empty\else%
    \ifx\psk@yAxisLabelPos\@empty\uput[90](#1,#4){\psk@yAxisLabel}%
    \else\rput{90}(\psk@yAxisLabelPos){\psk@yAxisLabel}%
    \fi%
  \fi%
  \ignorespaces%
}
\def\endpsgraph{%
  \pst@killglue
  \endpspicture%
  \endgroup%
}
\@namedef{psgraph*}{\psgraph*}
\@namedef{endpsgraph*}{\endpsgraph}
%
\define@key[psset]{pstricks-add}{ignoreLines}{\def\psk@ignoreLines{#1}}

\newcount\linecnt
\begingroup
\catcode`\,=13
\catcode`\_=13
\gdef\savedata@#1[#2]{%
  \xdef\pst@tempg{#2_}%
  \endgroup
  \let#1\pst@tempg
  \global\let\pst@tempg\relax
  \ignorespaces}
\gdef\readdata@{%
  \read1 to \pst@tempA
  \ifnum\linecnt=\psk@nStep
    \global\linecnt=0
    \expandafter\readdata@@\pst@tempA_\@nil
  \fi
  \global\advance\linecnt by 1
  \ifeof1\else\expandafter\readdata@\fi}
\gdef\pst@@readfile#1#2\@nil{\addto@pscode{,#1#2}}%
\gdef\readdata@@#1#2\@nil{\xdef\pst@tempg{\pst@tempg,#1#2}}%
\endgroup

\def\readdata{\@ifnextchar[{\readdata@i}{\readdata@i[]}}
\def\readdata@i[#1]#2#3{{%
  \def\pst@tempA{#1}%
  \ifx\pst@tempA\@empty\else\psset{#1}\fi
  \openin1=#3
  \begingroup
  \def\pst@tempg{}%
  \ifeof1
    \@pstrickserr{Data file `#3' not found.}\@ehpa
  \else
    \pst@datadelimiters
    \catcode`\[=1
    \catcode`\]=2
    \pst@cnta=0
    \loop \ifnum\the\pst@cnta<\psk@ignoreLines
      \advance\pst@cnta by 1\relax
      \read1 to \pst@tempA
    \repeat
    \ifnum\Pst@Debug>0 \typeout{>>> ignored \the\pst@cnta\space data lines}\fi%
    \global\linecnt=\psk@nStep%
    \readdata@%
  \fi%
  \endgroup%
  \global\let#2\pst@tempg%
  \global\let\pst@tempg\relax%
}\ignorespaces}
%
% D.G. addition - Jun.  9, 1998 - Polar plots using the \psplot macro
% Code added according the way suggested by Ulrich Dirr <udirr@das-team.com>

% For polar plots
\newif\ifpolarplot
\define@key[psset]{}{polarplot}[true]{\@nameuse{polarplot#1}}
%\psset{polarplot=false}
%
\newif\ifPst@algebraic%
\define@key[psset]{}{algebraic}[true]{\@nameuse{Pst@algebraic#1}}%
%\psset{dimen=middle}% remark of ML
%
\def\psplot@i#1#2#3{%
  \pst@killglue
  \begingroup
    \use@par
    \@nameuse{beginplot@\psplotstyle}%
% D.G. modification begin - Jun.  9, 1998
    \ifpolarplot
      \addto@pscode{%
        \psplot@init
        /x #1 def
        /x1 #2 def
        /dx x1 x sub \psk@plotpoints div def
        /F@pstplot \ifPst@algebraic (#3) tx@addDict begin AlgParser end cvx \else { #3 } \fi  def 
        /xy {% Adapted from \parametricplot@i
          F@pstplot x \ifPst@algebraic RadtoDeg \fi PtoC
%          #3 dup x cos mul exch x sin mul
          \pst@number\psyunit mul exch
          \pst@number\psxunit mul exch
        } def}%
    \else
% D.G. modification end
    \addto@pscode{%
      \psplot@init
      /x #1 def
      /x1 #2 def
      /dx x1 x sub \psk@plotpoints div def
      /F@pstplot \ifPst@algebraic (#3) tx@addDict begin AlgParser end cvx \else { #3 } \fi  def 
      /xy {
        x \pst@number\psxunit mul F@pstplot \pst@number\psyunit mul
%       \ifPst@algebraic F@pstplot \else #3 \fi \pst@number\psyunit mul
      } def}%
    \fi
    \gdef\psplot@init{}%
    \@pstfalse
    \@nameuse{testqp@\psplotstyle}%
    \if@pst
      \psplot@ii
    \else
      \psplot@iii
    \fi
  \endgroup
  \ignorespaces}
\def\parametricplot@i#1#2#3{%
  \pst@killglue%
  \begingroup
    \use@par
    \@nameuse{beginplot@\psplotstyle}%
    \addto@pscode{%
      \psplot@init
      /t #1 def
      /t1 #2 def
      /dt t1 t sub \psk@plotpoints div def
      \ifPst@algebraic/F@pstplot (#3) tx@addDict begin AlgParser end cvx def \fi
      /xy {
        \ifPst@algebraic F@pstplot \else #3 \fi
        \pst@number\psyunit mul exch
        \pst@number\psxunit mul exch
      } def}%
    \gdef\psplot@init{}%
    \@pstfalse
    \@nameuse{testqp@\psplotstyle}%
    \if@pst
      \parametricplot@ii
    \else
      \parametricplot@iii
    \fi
  \endgroup
  \ignorespaces}
%
\define@key[psset]{}{barwidth}{\pst@getlength{#1}\psk@barwidth}
%\psset{barwidth=0.25cm}
%
\def\psbar@ii{\addto@pscode{false \tx@NArray \psbar@iii}}
\def\psbar@iii{%
  newpath
  n { 
    /Yval exch def /Xval exch def 
    Xval \number\psk@barwidth 0.5 mul sub 0 moveto 
    0 Yval rlineto \number\psk@barwidth 0 rlineto 
    0 Yval neg rlineto \number\psk@barwidth neg 0 rlineto
  } repeat
}%
\def\beginplot@bar{\begin@SpecialObj}
\def\endplot@bar{%
  \psbar@ii\psk@fillstyle\ifpsshadow\pst@closedshadow\fi%
  \pst@stroke
  \end@SpecialObj%
}
%
\define@key[psset]{pstricks-add}{StepType}{\pst@expandafter\psset@@StepType{#1}\@nil}%
\def\psset@@StepType#1#2\@nil{%
  \ifx#1u\let\psk@StepType\@ne
  \else\ifx#1l\let\psk@StepType\z@\else\let\psk@StepType\tw@\fi\fi}
\psset{StepType=lower} % alternative StepType=upper StepType=Riemann
%
\def\psStep{\pst@object{psStep}}
\def\psStep@i(#1,#2)#3#4{%
  \begin@ClosedObj%
  \addto@pscode{
    \ifPst@algebraic /Func (#4) tx@addDict begin AlgParser end cvx def \fi 
    /x #1  def
    /dx #2 #1 sub #3 div def
    /scx { \pst@number\psxunit mul } def 
    /scy { \pst@number\psyunit mul } def
    \ifcase\psk@StepType % 0->lower
      x scx 0 moveto 
      #3 {
        \ifPst@algebraic Func \else #4 \fi scy dup x scx exch lineto 
        /x x dx add def
        x scx exch lineto x scx 0 lineto
      } repeat
    \or % 1-> upper
      x scx 0 moveto 
      #3 {
        /x x dx add def
        \ifPst@algebraic Func \else #4 \fi scy dup x dx sub scx exch lineto 
        x scx exch lineto x scx 0 lineto
      } repeat
    \or % 2-> Riemann
      /eps3 100 def
      /xMinMax [] def
      /AMax [] def
      /AMin [] def
      /dt dx eps3 div def
      #3 {
        /Max \ifPst@algebraic Func \else #4 \fi def 
        /Min Max def 
	/t x def % save x value
	eps3 {
	  \ifPst@algebraic Func \else #4 \fi 
	  dup
	  Max lt { /Max exch def } { dup Min gt { /Min exch def }{ pop } ifelse } ifelse
	  /x x dt add def
	} repeat 
	/x t def  % restore
	x scx Min scy Max scy xMinMax aload length 3 add array astore /xMinMax exch def
        /x x dx add def
      } repeat
      /dx dx scx def
      xMinMax aload length 3 div cvi { 
        /yMax ED /yMin ED /x ED 
	x yMin moveto dx 0 rlineto x dx add yMax lineto 
	dx neg 0 rlineto x yMin lineto } repeat
    \fi
  }%
  \psk@fillstyle
  \pst@stroke
  \end@ClosedObj%
}
%
\define@key[psset]{pstricks-add}{Derive}{\def\psk@Derive{#1}}%
%
%% #1 : x value
%% #2 : delta x
%% #3 : function
\def\psplotTangent{\pst@object{psplotTangent}}%  idea from Dominique Rodriguez
\def\psplotTangent@i#1#2#3{%
  \begin@OpenObj%
%  \let\pst@linetype\pst@arrowtype%
%  \pst@addarrowdef%
  \addto@pscode{
    gsave % save current state
    /F@pstplot \ifPst@algebraic (#3) tx@addDict begin AlgParser end cvx \else { #3 } \fi def % define function
    \ifx\psk@Derive\@empty\else 
      /FDer@pstplot % do we have a derivation defined?
        \ifPst@algebraic (\psk@Derive) tx@addDict begin AlgParser end cvx \else { \psk@Derive } \fi def % define derivation
    \fi
    % first we calculate the origin
    #1 dup /x ED /t ED tx@addDict begin mark F@pstplot end counttomark 1 gt % test, if we have parametricplot 
      { /y ED /x ED } % if yes, then we have 2 values
      { \ifpolarplot x \ifPst@algebraic RadtoDeg \fi PtoC /y ED /x ED \else /y ED \fi } ifelse 
    cleartomark 
    x \pst@number\psxunit mul y \pst@number\psyunit mul 
    translate % define the temporary origin
    % now we calculate the slope of the tangent 
    \ifx\psk@Derive\@empty% de we have a derivation defined?
    #1 abs 1.0e-6 lt % no, we choose secant for the tangent 
      { #1 0.0005 add dup /x ED /t ED tx@addDict begin mark F@pstplot end counttomark 1 gt % test, if we have parametricplot
        { /y2 ED /x2 ED }  % we have 2 values
        { \ifpolarplot dup x \ifPst@algebraic RadtoDeg \fi 
	  cos mul /x2 ED x \ifPst@algebraic RadtoDeg \fi sin mul \else /x2 x def \fi /y2 ED } ifelse
        cleartomark % delete the mark
        #1 0.0005 sub dup /x ED /t ED tx@addDict begin mark F@pstplot end counttomark 1 gt % test, if we have parametricplot
          { /y1 ED /x1 ED }
	  { \ifpolarplot dup x \ifPst@algebraic RadtoDeg \fi 
	    cos mul /x1 ED x \ifPst@algebraic RadtoDeg \fi sin mul \else /x1 x def \fi /y1 ED } ifelse
         cleartomark 
        y2 y1 sub x2 x1 sub } % dy dx
      {  % > 1.0e-06
        #1 1.0005 mul dup /x ED /t ED tx@addDict begin mark F@pstplot end counttomark 1 gt % test, if we have parametricplot 
          { /y2 ED /x2 ED } % we have 2 values
          { \ifpolarplot dup x \ifPst@algebraic RadtoDeg \fi 
	    cos mul /x2 ED x \ifPst@algebraic RadtoDeg \fi sin mul \else /x2 x def \fi /y2 ED } ifelse
	cleartomark 
        #1 .9995 mul dup /x ED /t ED tx@addDict begin mark F@pstplot end counttomark 1 gt % test, if we have parametricplot 
          { /y1 ED /x1 ED } % we have 2 values 
          { \ifpolarplot dup x \ifPst@algebraic RadtoDeg \fi 
	    cos mul /x1 ED x \ifPst@algebraic RadtoDeg \fi sin mul \else /x1 x def \fi /y1 ED } ifelse
	cleartomark 
        y2 y1 sub \pst@number\psyunit mul x2 x1 sub \pst@number\psxunit mul } ifelse 
      atan %  atan(dy dx), we have the slope angle of the secant
    \else % there is a derivation defined
    #1 dup /x ED /t ED tx@addDict begin mark FDer@pstplot end counttomark 1 gt % test, if we have parametricplot 
      { /y ED /x ED }
      { \ifpolarplot /Fphi ED % the value F'(phi) 
           tx@addDict begin F@pstplot end x \ifPst@algebraic RadtoDeg \fi PtoC /y0 ED /x0 ED % the x y values
           x \ifPst@algebraic RadtoDeg \fi sin Fphi mul x0 add /y ED 
           x \ifPst@algebraic RadtoDeg \fi cos Fphi mul y0 sub /x ED 
      \else /y ED /x 1 def \fi } ifelse
    cleartomark 
    y \pst@number\psyunit mul x \pst@number\psxunit mul Atan 
%    y ATAN1  % we have the slope angle of the tangent. ATAN is defined int the pstricks.pro, patch 6
    \fi
    rotate 					% rotate, depending to the origin
    /Lineto /lineto load def
    [
    -#2 \pst@number\psxunit mul 0 		% moveto
     #2 \pst@number\psxunit mul 0 		% lineto
    \pst@cp					% kill the currentpoint, if any
    false					% don't show the points
    \tx@Line
%      ArrowA CP 4 2 roll ArrowB L          	% the line with arrows L is defined in pstricks.pro
%     \pst@number\pslinewidth SLW		% set linewidth in pt
%     \@nameuse{psls@\pslinestyle}           	% linestyle
%     \pst@usecolor\pslinecolor			% linecolor
    stroke					% stroke everything
    \ifshowpoints 				% show the points?
      \psk@dotsize
      \@nameuse{psds@\psk@dotstyle}%
      0 0 Dot
    \fi		
    grestore					% restore old graphics state
   }%
  \use@pscode					% part of \end@OpenObj
  \endgroup%					% part of \end@OpenObj
  \ignorespaces%				% part of \end@OpenObj
}%
%
\define@key[psset]{}{method}{\def\psk@method{#1}}%     	   adams - rk4
\define@key[psset]{}{whichabs}{\def\psk@whichabs{#1}}%
\define@key[psset]{}{whichord}{\def\psk@whichord{#1}}%
\define@key[psset]{}{plotfuncx}{\def\psk@plotfuncx{#1}}%
\define@key[psset]{}{plotfuncy}{\def\psk@plotfuncy{#1}}%
\define@key[psset]{}{expression}{\def\psk@expression{#1}}%
\newif\ifPst@buildvector%
\define@key[psset]{}{buildvector}[true]{\@nameuse{Pst@buildvector#1}}%
\def\@rkiv{rk4}%		Runge-Kutta 4  method
\def\@adams{adams}%		Adams method
%
%% #1-#2 x range
%% #3 initial value of y (which is a vector) y(0) y'(0) y''(0) ...
%% #4 value of the derivative (y and t can be used)
\def\psplotDiffEqn{\def\pst@par{}\pst@object{psplotDiffEqn}}% initial code by Dominique 2005-05-21
\def\psplotDiffEqn@i#1#2#3#4{%
  \pst@killglue%
  \begingroup%
  \use@par%
  \@nameuse{beginplot@\psplotstyle}%
  \addto@pscode{%
    /x #1 def				% first value
    /x1 #2 def				% last value
    /y [ #3 ] def			% values for t=0
    /ylength y length def		% number of elements in #3
    /addvect { 
      1 1 ylength { 
        /i exch def 
	ylength i sub 2 add -1 roll add ylength 2 mul i sub 1 roll 
      } for 
    } def
    /dx x1 x sub \psk@plotpoints\space div def
    /mulvect { 
      ylength exch 
      1 index { 
        dup 4 -1 roll mul 2 index 2 add 1 roll 
      } repeat 
      pop pop } def
    /divvect { ylength exch 1 index { dup 4 -1 roll exch div 2 index 2 add 1 roll } repeat pop pop } def
    /k0 0 def /k1 0 def /k2 0 def /k3 0 def
    \ifPst@algebraic /F@pstplot (#4) tx@addDict begin AlgParser end cvx def \fi
    /Func { 
      \ifPst@algebraic F@pstplot ylength array astore 
      \else
        \ifPst@buildvector\else y aload pop \fi #4
        \ifPst@buildvector\else ylength array astore \fi
      \fi
    } def
    \ifx\psk@method\@adams /F1 0 def /F2 0 def /F3 0 def /F4 0 def /F5 0 def /F6 0 def /INIT 0 def \fi
    \ifx\psk@method\@empty\else			%% RUNGE-KUTTA & ADAMS  methods
      /RK {
         /k0 Func { dx mul } forall ylength array astore def 				%% y
         dup aload pop k0 { 2 div } forall addvect ylength array astore /y exch def %
         x dup dx 2 div add /x exch def 						%% y x
         /k1 Func { dx mul } forall ylength array astore def 				%% y x
         exch dup aload pop k1 { 2 div } forall addvect y astore pop 			%% x y
         /k2 Func { dx mul } forall ylength array astore def 				%% x y
         dup aload pop k2 aload pop addvect y astore pop exch dup dx add /x exch def 	%% y x
         /k3 Func { dx mul } forall ylength array astore def %% y x
         /x exch def 									%% y
         dup aload pop k0 aload pop k1 aload pop k2 aload pop addvect
         2 mulvect addvect k3 aload pop addvect
         6 divvect addvect y astore pop 
      } def
      \ifx\psk@method\@adams
         /ADAMS {
           %% ORDRE 4
           %%  F4 aload pop  55  mulvect
           %%  F3 aload pop -59 mulvect addvect
           %%  F2 aload pop  37  mulvect addvect
           %%  F1 aload pop  -9  mulvect addvect
           %%  dx mulvect 24 divvect
           %% ORDRE 5
           %%  F5 aload pop  1901  mulvect
           %%  F4 aload pop -2774  mulvect addvect
           %%  F3 aload pop  2616  mulvect addvect
           %%  F2 aload pop -1274  mulvect addvect
           %%  F1 aload pop   251  mulvect addvect
           %%  dx mulvect 720 divvect
           %% ORDRE 6
           F6 aload pop  4277  mulvect
           F5 aload pop -7923  mulvect addvect
           F4 aload pop  9982  mulvect addvect
           F3 aload pop -7298  mulvect addvect
           F2 aload pop  2877  mulvect addvect
           F1 aload pop  -475  mulvect addvect
           dx mulvect 1440 divvect
           y aload pop addvect ylength array astore /y exch def } def
       \fi
    \fi
    /xy {
      \ifx\psk@plotfuncx\@empty
        \ifx\psk@whichabs\@empty x \else y \psk@whichabs\space get \fi
      \else \psk@plotfuncx\space \fi 
      \pst@number\psxunit mul y
      \ifx\psk@method\@empty							%% EULER method
        /y Func { dx mul } forall y aload pop addvect ylength array astore def
      \else%
        \ifx\psk@method\@rkiv							%% RUNGE-KUTTA method
	  RK
        \else									%% ADAMS method
          /F1 F2 def /F2 F3 def /F3 F4 def /F4 F5 def /F5 F6 def /F6 Func def
          INIT 5 lt
          { RK /INIT INIT 1 add def }
          { ADAMS } ifelse
        \fi
      \fi
      \ifx\psk@plotfuncy\@empty 
        \ifx\psk@whichord\@empty 0 \else \psk@whichord\space \fi  get %
      \else \psk@plotfuncy\space \fi 
      \pst@number\psyunit mul
    } def
  }%
  \gdef\psplot@init{}%
  \@pstfalse
  \@nameuse{testqp@\psplotstyle}%
  \if@pst\psplot@ii\else\psplot@iii\fi
  \endgroup%
  \ignorespaces%
}
%
\def\psGTriangle{\pst@object{psGTriangle}}
\def\psGTriangle@i(#1)(#2)(#3)#4#5#6{{%
  \def\solid@star{}%
  \begin@ClosedObj
  \pst@getcoor{#1}\pst@tempA%   A: "rgb xr xg xb" or "gray xg"
  \pst@getcoor{#2}\pst@tempB%   B
  \pst@getcoor{#3}\pst@tempC%   C
  \pst@getcolor{#4}\pst@colorA
  \pst@getcolor{#5}\pst@colorB
  \pst@getcolor{#6}\pst@colorC
  \addto@pscode{%
    \pst@tempC		    % C
    \pst@tempB		    % B
    \psk@gangle             %   rotating angle
    \pst@tempA 		    % A, temporary origin
    /rgb {} def
    /gray {} def
    [ \pst@colorC ] aload length 1 eq { dup dup } if 3 array astore % gray -> rgb
    [ \pst@colorB ] aload length 1 eq { dup dup } if 3 array astore
    [ \pst@colorA ] aload length 1 eq { dup dup } if 3 array astore
    tx@addDict begin GTriangle end % PS part
  }%
  \if@star\pspolygon(#1)(#2)(#3)\fi%	draw borderline
  \def\pst@linetype{2}%
  \end@ClosedObj%
}}
%
\def\resetOptions{%
  \@zero=0%
%  \def\pshlabel##1{$##1$}%
%  \def\psvlabel##1{$##1$}%
  \psset{%
%%%% pstricks %%%%%%%%
  unit=1cm,%
  swapaxes=false,%
  showpoints=false,%
  border=0pt, bordercolor=white,%
  doubleline=false, doublesep=1.25\pslinewidth,%
  doublecolor=white,%
  shadow=false, shadowsize=3pt, shadowangle=-45, shadowcolor=darkgray,%
  linewidth=.8pt,%
  linecolor=black,%
  maxdashes=11, dash=5pt 3pt, dashadjust=true, %
  dotsep=3pt,%
  linestyle=solid,%
  fillcolor=white,%
  hatchwidth=.8pt, hatchsep=4pt, hatchcolor=black, hatchangle=45,%
  hatchsepinc=0pt,hatchwidthinc=0pt,%
  fillstyle=none,%
  nArrows=2,%
  arrows=-, arrowscale=1, arrowsize=1.5pt 2, arrowlength=1.4, arrowinset=.4,%
  tbarsize=2pt 5,%
  bracketlength=.15, rbracketlength=.15,%
  hooklength=3mm,hookwidth=1mm,
  ArrowFill=true,%
  ArrowInside={},ArrowInsidePos=0.5,%
  ArrowInsideNo=1,ArrowInsideOffset=0,%
 liftpen=0, linetype=0,%
  gangle=0,%
  curvature=1 .1 0,%
  dotsize=2pt 2,%
  dotangle=0, dotscale=1, dotstyle=*,%
  linearc=0pt,%
  framearc=0,%
  cornersize=relative,%
  dimen=middle,%
  gridwidth=.8pt, griddots=0, gridcolor=black,%
  subgridwidth=.4pt, subgridcolor=gray, subgriddots=0, subgriddiv=5,%
  gridlabels=10pt, gridlabelcolor=black,%
  framesep=3pt, boxsep=true,%
  trimode=U,%
  arcsep=0,radius=.25cm,%
  ref=c,rot=0,labelsep=5pt,refangle=0,%
  intSeparator={,},%
%%%%%%%%% pst-plot %%%%%%%%%%%%%
  StepType=lower, % alternative SumType=upper
  plotstyle=line,plotpoints=50,%
  ticksize=-4pt 4pt,tickstyle=full,ticks=all,%
  subticksize=0.75,subticks=1,tickcolor=black,%
  ticklinestyle=solid,subticklinestyle=solid,%
  subtickcolor=gray,%
  tickwidth=0.5\pslinewidth,subtickwidth=0.25\pslinewidth,%
  labels=all,Ox=0,Dx=1,dx=0,Oy=0,Dy=1,dy=0,%
  xlabelFactor=\relax,ylabelFactor=\relax,%
  showorigin=true,%
  axesstyle=axes,%
  ChangeOrder=false,%
  braceWidth=0.35,bracePos=0.5,%
  arrowscale=1,%
  dashColorI=black,dashColorII=red,dashNo=0.2,linecap=0,%
  wBegin=\pslinewidth, wEnd=\pslinewidth,%
  xyAxes=true,%
  trigLabels=false,%
  xDecimals={},yDecimals={},%
%  xLabel={},yLabel={},%
  xlogBase={},ylogBase={},%
  logLines=none,%
  ignoreLines=0,%
  nStep=1,nStart=0,nEnd={},%
  xStep=0,yStep=0,xStart={},xEnd={},yStart={},yEnd={},comma=false,%
  plotNo=1,plotNoMax=1,%
  xAxisLabel=x,yAxisLabel=y,%
  yAxisLabelPos={},xAxisLabelPos={},%
  llx=\z@, lly=\z@, urx=\z@, ury=\z@,% prevents rounding errors 
  randomPoints=1000,color=false,%
  method={},whichabs={},whichord={},%
  plotfuncx={},plotfuncy={},buildvector=false,algebraic=false,
  Derive={},%
%%%%%%%%% pst-node %%%%%%%%%%
  lineAngle=0,%
  nodealign=false,%
  href=0,%
  vref=.7ex,%
  framesize=10pt,%
  nodesep=0pt,%
  arm=10pt,%
  offset=0pt,%
  angle=0,%
  arcangle=8,%
  ncurv=.67,%
  loopsize=1cm,%
  boxsize=.4cm,%
  nrot=0,%
  npos=,%
  tpos=0.5,%
  shortput=none,%
  colsep=1.5cm,%
  rowsep=1.5cm,%
%  shortput=tablr,%%
  mcol=c,%
  mnode=R,%
  emnode=none}
}
%
\resetOptions
%
\catcode`\@=\PstAtCode\relax
%
%% END: pstricks-add.tex
\endinput
